diff --git "a/data.jsonl" "b/data.jsonl"
new file mode 100644--- /dev/null
+++ "b/data.jsonl"
@@ -0,0 +1,1000 @@
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, b: 1, y: 1, t: 1, k: 2}, what is the expected number of times the pattern 'ty*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, q: 4}, what is the expected number of times the pattern 'q+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, w: 1, x: 3}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, a: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, c: 1, g: 1, z: 1, a: 2}, what is the expected number of times the pattern 'zc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, n: 4}, what is the expected number of times the pattern 'gn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, a: 1, y: 2, t: 1}, what is the expected number of times the pattern 'a*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 4, j: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, x: 1, t: 3}. What is the expected number of occurrences of the pattern 'px*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'ge*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, n: 1, v: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 4, r: 2} to form a word, what is the expected number of matches of the pattern 'm*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, g: 4}, what is the expected number of times the pattern 'kg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, u: 2, z: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'zu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, m: 2, i: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'k*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, w: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'q*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, k: 1, y: 2, s: 1}. What is the expected number of occurrences of the pattern 's.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, x: 3}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, d: 3}. What is the expected number of occurrences of the pattern 'd.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, y: 4}. What is the expected number of occurrences of the pattern 'v*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, v: 3, k: 2}, what is the expected number of times the pattern 'v+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, b: 5} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, z: 1, h: 1, r: 1, m: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, b: 2, k: 1, d: 1, p: 1}. What is the expected number of occurrences of the pattern 'pk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, r: 1, c: 2, w: 1, l: 1}, what is the expected number of times the pattern 'i+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, r: 2, v: 1, n: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'ng+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, u: 1, k: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, n: 2, b: 1}. What is the expected number of occurrences of the pattern 'wn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, o: 1, q: 1, i: 3} to form a word, what is the expected number of matches of the pattern 't.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, r: 1, v: 1, d: 2, w: 1}. What is the expected number of occurrences of the pattern 'vr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, q: 2, h: 1, e: 1, t: 1} to form a word, what is the expected number of matches of the pattern 't*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, q: 3, z: 1, s: 1}. What is the expected number of occurrences of the pattern 'zq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'l.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 4, o: 2} to form a word, what is the expected number of matches of the pattern 'on*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, a: 1, h: 1, y: 3} to form a word, what is the expected number of matches of the pattern 'y*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, d: 1, k: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, p: 3, r: 2} to form a word, what is the expected number of matches of the pattern 'pr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, h: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'hz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, f: 1, g: 3}, what is the expected number of times the pattern 'gf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, e: 3, w: 1}, what is the expected number of times the pattern 'ow+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, j: 2, f: 1}, what is the expected number of times the pattern 'af+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 4, s: 2} to form a word, what is the expected number of matches of the pattern 's+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, a: 3}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, h: 3, b: 1}, what is the expected number of times the pattern 'h*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, f: 4}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, b: 5}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, e: 2, b: 1, h: 1, c: 1}, what is the expected number of times the pattern 'e.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 5, q: 1}, what is the expected number of times the pattern 'q.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, j: 4}. What is the expected number of occurrences of the pattern 'j+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, p: 3, m: 1, t: 1}, what is the expected number of times the pattern 't.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, x: 3, v: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, q: 1, f: 1, x: 1} to form a word, what is the expected number of matches of the pattern 't+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, y: 1, z: 1, r: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, u: 1, b: 1, h: 1, a: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, t: 3}, what is the expected number of times the pattern 'lt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, t: 2, d: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, o: 2, a: 2}, what is the expected number of times the pattern 'd*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, g: 1, e: 1, n: 2, o: 1}, what is the expected number of times the pattern 'gg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 2, g: 2, r: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, g: 3}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, y: 1, f: 2, s: 1, t: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, j: 2, z: 3} to form a word, what is the expected number of matches of the pattern 'pz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, i: 1, u: 2, o: 1, w: 1}, what is the expected number of times the pattern 'oi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, l: 2, j: 3}. What is the expected number of occurrences of the pattern 'j.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, n: 3, f: 1, z: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, i: 2, d: 2, y: 1}, what is the expected number of times the pattern 'yi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 4, w: 2}, what is the expected number of times the pattern 'wd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, a: 1, t: 1, w: 1, o: 2}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, p: 2, k: 3} to form a word, what is the expected number of matches of the pattern 'kh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, o: 1, x: 3, l: 1}. What is the expected number of occurrences of the pattern 'l+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, o: 1, a: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'sa+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, d: 4}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, b: 2, y: 1}, what is the expected number of times the pattern 'r*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, h: 1, w: 1, v: 1, k: 1}. What is the expected number of occurrences of the pattern 'cv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, c: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'jx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, g: 2, u: 3}. What is the expected number of occurrences of the pattern 'u*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, o: 2, u: 2, t: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 4, q: 2}, what is the expected number of times the pattern 'qh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, s: 3, b: 1, y: 1}. What is the expected number of occurrences of the pattern 'yq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, u: 3, p: 2}. What is the expected number of occurrences of the pattern 'hp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, y: 3, m: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, h: 1, y: 1, c: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'w*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, r: 1, t: 1, v: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'tn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, f: 2, s: 2, a: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, u: 1, t: 2} to form a word, what is the expected number of matches of the pattern 't+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, h: 1, m: 1, x: 1, d: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, d: 1, r: 1, h: 2, g: 1}, what is the expected number of times the pattern 'rd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, t: 1, b: 2, s: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, c: 1, u: 2, x: 1} to form a word, what is the expected number of matches of the pattern 'u.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, n: 1, u: 2, h: 2}, what is the expected number of times the pattern 'u*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 4, e: 1, f: 1}, what is the expected number of times the pattern 'fx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, i: 1, f: 2, q: 1, a: 1}, what is the expected number of times the pattern 'ai+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, l: 3}. What is the expected number of occurrences of the pattern 'l.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, q: 2, f: 2, d: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, c: 3, t: 2} to form a word, what is the expected number of matches of the pattern 'ct+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, k: 1, z: 2, y: 1, b: 1}. What is the expected number of occurrences of the pattern 'k+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 4, f: 1, b: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, v: 1, q: 1, k: 1, a: 1}, what is the expected number of times the pattern 'qt*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, a: 3}. What is the expected number of occurrences of the pattern 'f+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 4, u: 1, s: 1}, what is the expected number of times the pattern 'f*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, v: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'm.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, c: 3}, what is the expected number of times the pattern 'gc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, f: 1, u: 2, e: 2}. What is the expected number of occurrences of the pattern 'h*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, x: 2, i: 1, z: 1, d: 1}. What is the expected number of occurrences of the pattern 'di+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, u: 1, k: 2}, what is the expected number of times the pattern 'p+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, l: 1, x: 1, h: 2, t: 1}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, n: 3, y: 1}, what is the expected number of times the pattern 'yo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, c: 3, j: 1}. What is the expected number of occurrences of the pattern 'j.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, l: 1, p: 1, m: 1, k: 2}. What is the expected number of occurrences of the pattern 'lk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, s: 1, t: 1, l: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, w: 2, f: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'w.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, s: 1, n: 1, c: 1, k: 2}, what is the expected number of times the pattern 'n+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, m: 1, y: 3}, what is the expected number of times the pattern 'y+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, w: 3}. What is the expected number of occurrences of the pattern 'xw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, o: 3}. What is the expected number of occurrences of the pattern 'zo*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 4, p: 2}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, g: 1, k: 1, d: 2}. What is the expected number of occurrences of the pattern 'g*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, y: 1, h: 1, b: 1, f: 2}, what is the expected number of times the pattern 'w*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, z: 1, l: 2, g: 1}, what is the expected number of times the pattern 'l+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, n: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'on+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, i: 1, m: 2}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, g: 2, s: 1, x: 1}. What is the expected number of occurrences of the pattern 'g*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, w: 4}. What is the expected number of occurrences of the pattern 'w*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, x: 1, r: 3}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, n: 3, j: 1} to form a word, what is the expected number of matches of the pattern 'n+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, x: 5} to form a word, what is the expected number of matches of the pattern 'xr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, d: 1, y: 2, e: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, o: 2, b: 2}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, g: 2, m: 1, k: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, t: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'k+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, i: 1, g: 1, u: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, a: 2, p: 1, x: 1, q: 1}. What is the expected number of occurrences of the pattern 'x*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, h: 1, y: 2}, what is the expected number of times the pattern 'h.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, s: 1, b: 1, o: 2, i: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, b: 3, x: 1, e: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, y: 1, u: 1, n: 3}, what is the expected number of times the pattern 'y.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, l: 2, n: 2, u: 1}, what is the expected number of times the pattern 'un*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, l: 3} to form a word, what is the expected number of matches of the pattern 'q.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, m: 2, i: 3}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, m: 2, d: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'dm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, t: 3}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, f: 2, v: 1, i: 1, w: 1}, what is the expected number of times the pattern 'v*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 4, t: 2} to form a word, what is the expected number of matches of the pattern 'pt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, g: 1, n: 1, y: 2, r: 1}, what is the expected number of times the pattern 'g+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, k: 3} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, z: 1, f: 3}. What is the expected number of occurrences of the pattern 'hf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, c: 5} to form a word, what is the expected number of matches of the pattern 'c+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, s: 1, q: 1, n: 2, a: 1}, what is the expected number of times the pattern 'q.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 4, y: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'k*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'i.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, n: 1, x: 4} to form a word, what is the expected number of matches of the pattern 'n.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, d: 2, z: 2}. What is the expected number of occurrences of the pattern 'd*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, g: 1, i: 1, w: 3} to form a word, what is the expected number of matches of the pattern 'w*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, q: 2, m: 2}, what is the expected number of times the pattern 'qg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, m: 3, b: 1}. What is the expected number of occurrences of the pattern 'm.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'he+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, m: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'xt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 2, w: 1, m: 2, b: 1}. What is the expected number of occurrences of the pattern 'd*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, c: 1, y: 1, b: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'y.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, m: 3, x: 1} to form a word, what is the expected number of matches of the pattern 'x.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'y*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, s: 1, q: 1, f: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, w: 1, b: 2, a: 1, m: 1}, what is the expected number of times the pattern 'w+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, n: 1, z: 1, a: 2, v: 1}. What is the expected number of occurrences of the pattern 'v.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, c: 2, a: 1, z: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, r: 2, b: 1, q: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, k: 3, l: 2}. What is the expected number of occurrences of the pattern 'kl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, f: 1, q: 1, p: 2, u: 1}. What is the expected number of occurrences of the pattern 's.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, e: 2, t: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, o: 2, f: 2}. What is the expected number of occurrences of the pattern 'm+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, x: 1, m: 1, h: 1, v: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, g: 3, c: 1}, what is the expected number of times the pattern 'g+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 4, u: 2}. What is the expected number of occurrences of the pattern 'q+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, f: 3} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, z: 2, j: 1, r: 1, m: 1}, what is the expected number of times the pattern 'rz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, b: 4}, what is the expected number of times the pattern 'g+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, y: 4}. What is the expected number of occurrences of the pattern 'y.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, n: 1, h: 1, e: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'en+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, b: 1, v: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'x.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, c: 1, q: 1, e: 1, t: 2}, what is the expected number of times the pattern 'qc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, b: 5}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, o: 1, n: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'oa+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 5, v: 1}, what is the expected number of times the pattern 'c+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, j: 1, s: 4} to form a word, what is the expected number of matches of the pattern 'gs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, d: 2, g: 3} to form a word, what is the expected number of matches of the pattern 'gn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 5, z: 1}, what is the expected number of times the pattern 'z*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, l: 4}, what is the expected number of times the pattern 'l.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 4, b: 2} to form a word, what is the expected number of matches of the pattern 'p.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, q: 1, v: 1, m: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, q: 2, m: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, a: 2, j: 1, h: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, s: 1, f: 1, t: 1, g: 1}, what is the expected number of times the pattern 'tf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, d: 2, l: 1, c: 1}. What is the expected number of occurrences of the pattern 'cl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, e: 1, j: 1, w: 1, u: 2}. What is the expected number of occurrences of the pattern 'x+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, x: 2, n: 2}, what is the expected number of times the pattern 'w*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, t: 1, g: 1, y: 1, w: 2} to form a word, what is the expected number of matches of the pattern 't+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, t: 2, l: 1, x: 1, c: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, k: 3, d: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'z+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, d: 3}, what is the expected number of times the pattern 'dm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, e: 1, b: 1, i: 3}. What is the expected number of occurrences of the pattern 'f+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, h: 1, z: 2, w: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, q: 2, g: 1, b: 1}, what is the expected number of times the pattern 'gg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, e: 2, s: 1}. What is the expected number of occurrences of the pattern 'q*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, g: 1, l: 1, s: 2, i: 1}. What is the expected number of occurrences of the pattern 's.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, c: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'ac+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, n: 2, o: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'o*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, s: 2, m: 2}, what is the expected number of times the pattern 'r+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, o: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, s: 3} to form a word, what is the expected number of matches of the pattern 'f.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, d: 3}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, n: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, z: 3}, what is the expected number of times the pattern 'zn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, u: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'n+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, o: 3, e: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, e: 3}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, b: 1, r: 2, g: 2}. What is the expected number of occurrences of the pattern 'r.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, t: 3}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, a: 1, p: 2, r: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'p+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, o: 1, e: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'o+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, r: 3}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, b: 1, x: 2, u: 2}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, h: 1, p: 2, e: 1}. What is the expected number of occurrences of the pattern 'pt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, d: 3}, what is the expected number of times the pattern 'u*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 4, d: 2}, what is the expected number of times the pattern 'd.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 4, y: 1, l: 1}, what is the expected number of times the pattern 'l.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, j: 2, s: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, o: 2, j: 1, g: 1, v: 1}, what is the expected number of times the pattern 'j.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, v: 1, m: 2, k: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'd.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, o: 1, g: 1, h: 2}, what is the expected number of times the pattern 'o*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, a: 3, r: 1, w: 1}. What is the expected number of occurrences of the pattern 'ra+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, a: 1, l: 2, s: 1}. What is the expected number of occurrences of the pattern 'q.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, i: 4}. What is the expected number of occurrences of the pattern 'i+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, m: 3}. What is the expected number of occurrences of the pattern 'im+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, k: 1, v: 1, r: 2, o: 1}. What is the expected number of occurrences of the pattern 'vk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, a: 2, x: 2}, what is the expected number of times the pattern 'a+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, a: 2, v: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'ua+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, o: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'on*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'uv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, j: 2, c: 2, v: 1}, what is the expected number of times the pattern 'j+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, c: 1, q: 1, j: 1, w: 2}. What is the expected number of occurrences of the pattern 'ch*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, c: 1, e: 3}. What is the expected number of occurrences of the pattern 'c*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, h: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, d: 1, b: 4}, what is the expected number of times the pattern 'k.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, x: 1, j: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, j: 1, f: 1, g: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, x: 3}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, o: 3}. What is the expected number of occurrences of the pattern 'oc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, v: 1, j: 2, w: 1}, what is the expected number of times the pattern 'mw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, m: 3, u: 1} to form a word, what is the expected number of matches of the pattern 'm.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, g: 3}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, v: 1, y: 1, t: 2, j: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, e: 2, u: 1, y: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'zu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, l: 1, z: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'l.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, k: 1, b: 2, s: 1, f: 1}, what is the expected number of times the pattern 'sf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, h: 1, e: 3, w: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, z: 1, n: 1, r: 2, j: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, i: 1, h: 1, t: 1, v: 1}, what is the expected number of times the pattern 'vh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, i: 1, d: 2, v: 1}, what is the expected number of times the pattern 'd+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, s: 1, f: 3}, what is the expected number of times the pattern 's+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, q: 1, w: 1, p: 1}. What is the expected number of occurrences of the pattern 'w+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, z: 3}, what is the expected number of times the pattern 'zo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, w: 4}. What is the expected number of occurrences of the pattern 'w.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, x: 2, k: 1, b: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'xx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 4, k: 2}, what is the expected number of times the pattern 'ks+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, t: 1, d: 1, q: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'gq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, s: 3, p: 1, k: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, e: 1, c: 2, x: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, l: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'y+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 4, y: 2}, what is the expected number of times the pattern 'y+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, m: 1, z: 1, y: 2, r: 1}. What is the expected number of occurrences of the pattern 'r+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, f: 3, j: 1, k: 1}. What is the expected number of occurrences of the pattern 'f+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 5, y: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 4, u: 2}. What is the expected number of occurrences of the pattern 'cu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, z: 1, u: 1, d: 1, i: 2}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, q: 2, i: 1, j: 2}. What is the expected number of occurrences of the pattern 'kj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, y: 1, u: 2, z: 2}. What is the expected number of occurrences of the pattern 'u*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'y.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, f: 3}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, d: 3, a: 1}. What is the expected number of occurrences of the pattern 'd+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, t: 3, u: 1} to form a word, what is the expected number of matches of the pattern 'y+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, d: 5}, what is the expected number of times the pattern 'dr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, j: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, m: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, h: 1, r: 1, j: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'w+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, p: 4} to form a word, what is the expected number of matches of the pattern 'p*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, o: 1, g: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'n.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 4, f: 2}. What is the expected number of occurrences of the pattern 'a*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, m: 1, s: 3, o: 1} to form a word, what is the expected number of matches of the pattern 's*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'r+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, b: 2, g: 1, i: 1, r: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, y: 2, n: 1, h: 1, c: 1}, what is the expected number of times the pattern 'ny*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 4, k: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, r: 4, q: 1} to form a word, what is the expected number of matches of the pattern 'dq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 4, a: 2}. What is the expected number of occurrences of the pattern 'ae+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, i: 2, h: 1, z: 1}. What is the expected number of occurrences of the pattern 'p+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, e: 4}, what is the expected number of times the pattern 'x.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, m: 1, l: 1, e: 1, h: 2}. What is the expected number of occurrences of the pattern 'eh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 5, s: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, p: 1, x: 1, y: 1, a: 1}, what is the expected number of times the pattern 'pa*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, j: 1, k: 2}, what is the expected number of times the pattern 'i+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, b: 2, a: 2}. What is the expected number of occurrences of the pattern 'pa+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, t: 3} to form a word, what is the expected number of matches of the pattern 't*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, h: 3, t: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, e: 2, n: 1, p: 1, x: 1}. What is the expected number of occurrences of the pattern 'n+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, m: 1, r: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'lm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, z: 2, s: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, w: 4}. What is the expected number of occurrences of the pattern 'q+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, v: 1, w: 3} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, k: 1, a: 1, o: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'a+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, j: 2, y: 1, l: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'y+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, g: 2, k: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, m: 3, y: 1}. What is the expected number of occurrences of the pattern 'j.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, k: 4} to form a word, what is the expected number of matches of the pattern 'k+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, w: 2, b: 2}. What is the expected number of occurrences of the pattern 'vb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, w: 3, u: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'x+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, t: 1, w: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, o: 2, m: 1, s: 2}. What is the expected number of occurrences of the pattern 's.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, b: 1, s: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'w+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, d: 1, x: 1, o: 2, j: 1}. What is the expected number of occurrences of the pattern 'xp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, h: 2}, what is the expected number of times the pattern 'h.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, a: 1, k: 1, u: 1, g: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, f: 2, w: 1, g: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, f: 2, e: 2, s: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, c: 1, k: 1, d: 1}. What is the expected number of occurrences of the pattern 'r*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 4, d: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 4, q: 2} to form a word, what is the expected number of matches of the pattern 'c.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, f: 1, p: 1, s: 3}, what is the expected number of times the pattern 'f+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, j: 2, f: 1, m: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, y: 1, n: 2}. What is the expected number of occurrences of the pattern 'ns+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, j: 2, f: 1}. What is the expected number of occurrences of the pattern 'jm+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, o: 1, j: 1, q: 1, v: 1}, what is the expected number of times the pattern 'v*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, r: 1, a: 2}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, v: 2, l: 1, m: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'mv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, r: 2, s: 1, g: 1, z: 1}, what is the expected number of times the pattern 'gz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 4, l: 1, e: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, l: 1, p: 1, j: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'r+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, r: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, m: 1, d: 2, p: 2}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 4, p: 2} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, f: 1, x: 2, e: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, k: 2, w: 2}. What is the expected number of occurrences of the pattern 'w*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, b: 2, z: 1, y: 1, a: 1}. What is the expected number of occurrences of the pattern 'y+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, f: 1, b: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'xx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, w: 4} to form a word, what is the expected number of matches of the pattern 'k*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 4, e: 2}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, x: 3, w: 1}. What is the expected number of occurrences of the pattern 'w+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, u: 2, s: 2}. What is the expected number of occurrences of the pattern 'u+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 5, y: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, w: 2, m: 2}. What is the expected number of occurrences of the pattern 'w+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, h: 2}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, j: 4, r: 1}, what is the expected number of times the pattern 'ra+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, b: 4} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, a: 3, s: 1, v: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, w: 1, l: 1, f: 1, x: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 5, f: 1}. What is the expected number of occurrences of the pattern 'fs+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, o: 3}, what is the expected number of times the pattern 'o*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, g: 1, j: 1, f: 1, e: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, g: 1, x: 1, h: 2, z: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, v: 2, o: 1, u: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, w: 4}. What is the expected number of occurrences of the pattern 'y*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, i: 2, z: 1, f: 1, a: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 4, j: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, k: 2, e: 3}, what is the expected number of times the pattern 'z+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, u: 2, m: 1, f: 1, z: 1}, what is the expected number of times the pattern 'if*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, c: 3}. What is the expected number of occurrences of the pattern 'c.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, b: 2, d: 2, p: 1}. What is the expected number of occurrences of the pattern 'lb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, z: 3}, what is the expected number of times the pattern 'c+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, z: 2, o: 1, n: 1, c: 1}, what is the expected number of times the pattern 'ro+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, x: 1, p: 2, r: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, r: 2, m: 2, d: 1}. What is the expected number of occurrences of the pattern 'h*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, u: 5}. What is the expected number of occurrences of the pattern 'up+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, b: 1, t: 1, c: 1, k: 2}, what is the expected number of times the pattern 'c.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, l: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'vl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, r: 2, i: 1, o: 1}, what is the expected number of times the pattern 'ir*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, t: 1, x: 1, d: 1, b: 2}. What is the expected number of occurrences of the pattern 'x+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, x: 1, y: 4}. What is the expected number of occurrences of the pattern 'xw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, d: 1, u: 2, p: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, l: 1, q: 3}. What is the expected number of occurrences of the pattern 'f+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, h: 2, a: 2, f: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, m: 1, x: 2, a: 1, y: 1}. What is the expected number of occurrences of the pattern 'a+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, n: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'j+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, b: 1, h: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'fq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 4, k: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, u: 1, k: 2, e: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 4, q: 2} to form a word, what is the expected number of matches of the pattern 'qs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 4, s: 2}. What is the expected number of occurrences of the pattern 's*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, r: 3}, what is the expected number of times the pattern 'r.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, w: 1, g: 1, i: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'lg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 4, i: 2}, what is the expected number of times the pattern 'fi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, w: 1, t: 1, a: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'e*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, j: 4}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, s: 3, x: 2} to form a word, what is the expected number of matches of the pattern 'j.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 4, d: 2}, what is the expected number of times the pattern 'e*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 4, a: 2}, what is the expected number of times the pattern 'sa*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, f: 2, e: 3}. What is the expected number of occurrences of the pattern 'e.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, e: 4}, what is the expected number of times the pattern 'eo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, y: 1, r: 2, c: 1, j: 1}, what is the expected number of times the pattern 'yj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, k: 1, b: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 3, j: 1, g: 1, c: 1}, what is the expected number of times the pattern 'g+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, o: 1, q: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'o+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, i: 2, d: 2}, what is the expected number of times the pattern 'di*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, k: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, a: 1, y: 2}. What is the expected number of occurrences of the pattern 'a+t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, c: 4} to form a word, what is the expected number of matches of the pattern 'c.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, b: 1, x: 2}. What is the expected number of occurrences of the pattern 'x.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 4, l: 1, w: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, w: 4}. What is the expected number of occurrences of the pattern 'ew*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, a: 1, i: 3, w: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, o: 2, p: 1, z: 2}, what is the expected number of times the pattern 'z.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, b: 1, s: 1, o: 1, u: 1}, what is the expected number of times the pattern 'jo+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, f: 1, t: 2}. What is the expected number of occurrences of the pattern 'f*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, y: 2, g: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 4, l: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, u: 2, j: 1, f: 1, m: 1}. What is the expected number of occurrences of the pattern 'u+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, g: 2, q: 1, p: 2}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, y: 1, n: 1, c: 1, z: 2}. What is the expected number of occurrences of the pattern 'c*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, l: 2, g: 1, d: 1}, what is the expected number of times the pattern 'f+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, e: 1, u: 1, x: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'e+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, s: 1, v: 3}, what is the expected number of times the pattern 's.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, d: 1, l: 1, e: 3}, what is the expected number of times the pattern 'hl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, v: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'v.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, o: 2, y: 2}. What is the expected number of occurrences of the pattern 'w+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, e: 1, c: 2}. What is the expected number of occurrences of the pattern 'ac+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, y: 4}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, g: 3}. What is the expected number of occurrences of the pattern 'ag+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, z: 5} to form a word, what is the expected number of matches of the pattern 'wz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, c: 1, p: 2, u: 1, v: 1}. What is the expected number of occurrences of the pattern 'up*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, l: 4}, what is the expected number of times the pattern 'lm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, w: 1, k: 1, f: 1, y: 2}, what is the expected number of times the pattern 'yf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, h: 4} to form a word, what is the expected number of matches of the pattern 'hx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, n: 4}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, l: 1, q: 1, h: 1, t: 1}. What is the expected number of occurrences of the pattern 'hq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, l: 2, g: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'l.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, w: 3, q: 2}, what is the expected number of times the pattern 'q*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 4, l: 2}, what is the expected number of times the pattern 'l+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, k: 3, q: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, f: 1, r: 1, m: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'x*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, d: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'x.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, q: 3} to form a word, what is the expected number of matches of the pattern 'w*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, u: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'au*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, n: 1, v: 2, k: 2}. What is the expected number of occurrences of the pattern 'n.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, d: 1, l: 3, x: 1} to form a word, what is the expected number of matches of the pattern 'lx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, m: 1, o: 2, w: 2}, what is the expected number of times the pattern 'o+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, r: 1, l: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 4, k: 2} to form a word, what is the expected number of matches of the pattern 'kh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, p: 3, t: 2}, what is the expected number of times the pattern 'p.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, c: 2, b: 1, f: 2}, what is the expected number of times the pattern 'c*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, w: 1, a: 1, i: 1, l: 1}, what is the expected number of times the pattern 'y.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, n: 3, a: 1}. What is the expected number of occurrences of the pattern 'na*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, x: 1, u: 1, e: 2}. What is the expected number of occurrences of the pattern 'x+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, n: 1, d: 3, c: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, e: 3, z: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, j: 3, s: 1, n: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, r: 1, o: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'w+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, k: 3, u: 2}. What is the expected number of occurrences of the pattern 'u*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, u: 2, k: 1, w: 1, j: 1}, what is the expected number of times the pattern 'p+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, c: 2, i: 1, s: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, m: 1, p: 1, b: 1, i: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, x: 2, y: 1, e: 1, v: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, e: 1, d: 2}. What is the expected number of occurrences of the pattern 'e*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, z: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, k: 2, u: 1, n: 1}. What is the expected number of occurrences of the pattern 'u.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, x: 2, a: 1, h: 1, u: 1}. What is the expected number of occurrences of the pattern 'q+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, g: 2, s: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, m: 2, q: 1, s: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, o: 3} to form a word, what is the expected number of matches of the pattern 'oz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, d: 1, k: 2, g: 1}, what is the expected number of times the pattern 'pk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, m: 1, v: 2, d: 2}. What is the expected number of occurrences of the pattern 'd.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, r: 5} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, b: 2, x: 2}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, z: 1, b: 1, q: 2}, what is the expected number of times the pattern 'zq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, a: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, e: 3} to form a word, what is the expected number of matches of the pattern 'e+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, e: 1, c: 1, j: 1, d: 1}. What is the expected number of occurrences of the pattern 'e+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, y: 3}. What is the expected number of occurrences of the pattern 'y+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, u: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'n.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, k: 1, a: 3}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, r: 1, i: 4}, what is the expected number of times the pattern 'ir*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, h: 2, d: 2}, what is the expected number of times the pattern 'h.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, e: 2, h: 1, f: 1}, what is the expected number of times the pattern 'e+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 4, u: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, o: 2, q: 1, b: 1}. What is the expected number of occurrences of the pattern 'u*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, s: 1, r: 1, y: 1, w: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, a: 4}, what is the expected number of times the pattern 'a+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, r: 1, z: 1, w: 1, x: 2}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 5, r: 1} to form a word, what is the expected number of matches of the pattern 'r*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, p: 3}. What is the expected number of occurrences of the pattern 'po+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, m: 1, q: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'qx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, y: 1, e: 1, k: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'y.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, v: 1, g: 2, l: 1, a: 1}. What is the expected number of occurrences of the pattern 'v.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, k: 2, g: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, x: 1, o: 1, q: 1, v: 1}. What is the expected number of occurrences of the pattern 't.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, i: 2, y: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'kt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, k: 1, h: 2, m: 1, o: 1}, what is the expected number of times the pattern 'm*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, b: 2, v: 2, o: 1}, what is the expected number of times the pattern 'o*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, w: 1, l: 1, d: 1, u: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, u: 3}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 4, u: 2} to form a word, what is the expected number of matches of the pattern 'x.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, n: 2, s: 1, b: 2}. What is the expected number of occurrences of the pattern 'g*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, l: 2, s: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'l.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, h: 1, p: 1, y: 3}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, w: 1, f: 1, z: 2}, what is the expected number of times the pattern 'qw+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, n: 2}, what is the expected number of times the pattern 'cn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, b: 1, t: 1, k: 3}, what is the expected number of times the pattern 'm.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, o: 2, i: 1, d: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'v.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, t: 3, n: 1, o: 1}, what is the expected number of times the pattern 'wn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, x: 1, f: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'h+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, m: 1, o: 1, i: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'r*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, p: 3, k: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, l: 3, g: 1}. What is the expected number of occurrences of the pattern 'ng+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, j: 4}, what is the expected number of times the pattern 'j.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, c: 1, y: 1, b: 1, f: 2}. What is the expected number of occurrences of the pattern 'y.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, u: 4, c: 1} to form a word, what is the expected number of matches of the pattern 'u+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, p: 3, d: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, r: 1, k: 3}. What is the expected number of occurrences of the pattern 'k*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, j: 2, c: 3}, what is the expected number of times the pattern 'j*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, n: 4}, what is the expected number of times the pattern 'n*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, w: 2, x: 2}, what is the expected number of times the pattern 'w+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, n: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'nb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, v: 2, o: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'o+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, x: 1, q: 1, v: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, w: 4} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, j: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, r: 1, b: 2, j: 1, e: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, t: 3}, what is the expected number of times the pattern 'm+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, m: 2, v: 1, o: 2}, what is the expected number of times the pattern 'v*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, v: 1, q: 3}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, i: 4}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, r: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'iy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, n: 1, i: 1, y: 1}. What is the expected number of occurrences of the pattern 'ny+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, n: 3}. What is the expected number of occurrences of the pattern 'nd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 4, f: 2}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, n: 1, c: 1, m: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, e: 1, x: 2}, what is the expected number of times the pattern 'm*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, z: 2, d: 1, e: 1}. What is the expected number of occurrences of the pattern 'jd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 3, q: 3} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, s: 1, y: 1, h: 3}, what is the expected number of times the pattern 'y.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, p: 2, j: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, x: 1, z: 1, w: 2, s: 1}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, c: 2, k: 1, u: 1, p: 1}, what is the expected number of times the pattern 'y*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, y: 1, v: 2, j: 2} to form a word, what is the expected number of matches of the pattern 'v+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 4, s: 2}. What is the expected number of occurrences of the pattern 'sx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, a: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'd+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, e: 2, o: 2}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, x: 1, w: 1, n: 2, v: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, o: 1, t: 1, i: 3}. What is the expected number of occurrences of the pattern 'i.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, n: 1, q: 2, l: 1, h: 1}, what is the expected number of times the pattern 'qk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, x: 3}, what is the expected number of times the pattern 'ax*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, c: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'rd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, z: 1, l: 2, m: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'vz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, e: 2, s: 2, g: 1}, what is the expected number of times the pattern 'e+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, n: 3, t: 1}, what is the expected number of times the pattern 't+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, g: 2, z: 3}. What is the expected number of occurrences of the pattern 'gu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 5, b: 1}. What is the expected number of occurrences of the pattern 'lb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.83", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, m: 2, a: 1, j: 1, d: 1}. What is the expected number of occurrences of the pattern 'v+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, w: 4}, what is the expected number of times the pattern 'w+z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 4, w: 2}. What is the expected number of occurrences of the pattern 'w+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, f: 1, i: 1, y: 1, x: 1}. What is the expected number of occurrences of the pattern 'i*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, n: 3, k: 1} to form a word, what is the expected number of matches of the pattern 'k+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, p: 3, m: 1, l: 1}. What is the expected number of occurrences of the pattern 'pl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, d: 1, f: 1, j: 1, s: 1}, what is the expected number of times the pattern 'e*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, h: 3} to form a word, what is the expected number of matches of the pattern 'hh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, d: 1, n: 2, p: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, p: 1, l: 2, o: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'g.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, e: 2, m: 2}. What is the expected number of occurrences of the pattern 'em*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, h: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'er*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, k: 1, s: 1, m: 2} to form a word, what is the expected number of matches of the pattern 's+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, f: 1, q: 3, c: 1} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, u: 1, o: 2, l: 2}, what is the expected number of times the pattern 'vl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, s: 1, j: 1, z: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'z.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, l: 2, b: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, i: 2, h: 1, g: 2}, what is the expected number of times the pattern 'i.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, q: 2, e: 2, s: 1}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, w: 1, q: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'x+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, o: 2, y: 3}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, t: 1, o: 1, s: 1, d: 2}. What is the expected number of occurrences of the pattern 'ts+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, r: 1, s: 1, a: 2}, what is the expected number of times the pattern 's.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, b: 1, n: 1, r: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, h: 1, q: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, d: 1, w: 3}, what is the expected number of times the pattern 'd+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, a: 2, m: 1, x: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'x*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, s: 3}, what is the expected number of times the pattern 's+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, b: 1, p: 1, r: 2, n: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'r.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, p: 1, h: 2, z: 1, c: 1}. What is the expected number of occurrences of the pattern 'hz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, m: 3} to form a word, what is the expected number of matches of the pattern 'im+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, s: 1, m: 1, c: 1, x: 2}, what is the expected number of times the pattern 's+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, i: 2, k: 1, d: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'ki*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, g: 2, a: 2, s: 1}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, n: 4} to form a word, what is the expected number of matches of the pattern 'ny+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, u: 3, s: 1, p: 1}. What is the expected number of occurrences of the pattern 'p*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 2, k: 1, h: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'k.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, c: 1, b: 1, p: 1, h: 2}. What is the expected number of occurrences of the pattern 'pc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 4, m: 2} to form a word, what is the expected number of matches of the pattern 'o+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, u: 2, d: 1}, what is the expected number of times the pattern 'm.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, k: 1, u: 2, c: 1}, what is the expected number of times the pattern 'ka*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, m: 2, l: 1, z: 1, e: 1}. What is the expected number of occurrences of the pattern 'c.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, e: 3, v: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, k: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, d: 1, r: 2, a: 2}, what is the expected number of times the pattern 'rx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, o: 1, v: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, h: 5}, what is the expected number of times the pattern 'nh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 4, x: 2}, what is the expected number of times the pattern 'r+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, s: 3}. What is the expected number of occurrences of the pattern 'g*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, e: 3, u: 2} to form a word, what is the expected number of matches of the pattern 'u.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 2, y: 1, a: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'ag*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, c: 1, t: 2, s: 2}. What is the expected number of occurrences of the pattern 's*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, h: 2, l: 1, k: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, e: 4}. What is the expected number of occurrences of the pattern 'k.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, o: 1, s: 1, r: 1, x: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, l: 1, b: 2, k: 1}, what is the expected number of times the pattern 'k*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, n: 2, d: 3}, what is the expected number of times the pattern 'e.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, h: 1, n: 1, c: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'c+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, y: 1, u: 3} to form a word, what is the expected number of matches of the pattern 'k*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, q: 1, r: 3}. What is the expected number of occurrences of the pattern 'q*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, a: 2, d: 2}, what is the expected number of times the pattern 'ax*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, o: 1, e: 1, c: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'w.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, m: 2, g: 1, t: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, m: 2}, what is the expected number of times the pattern 'am*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, z: 1, k: 1, e: 2, q: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, p: 3, c: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, a: 1, s: 3, x: 1} to form a word, what is the expected number of matches of the pattern 'g.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, x: 1, b: 1, p: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'pr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 4, w: 1, e: 1}. What is the expected number of occurrences of the pattern 'c*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, t: 4}, what is the expected number of times the pattern 'tu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, i: 5}. What is the expected number of occurrences of the pattern 'm+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, p: 3}. What is the expected number of occurrences of the pattern 'pi*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, e: 1, y: 2, i: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, b: 1, r: 3}, what is the expected number of times the pattern 'qq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, x: 2, w: 1}, what is the expected number of times the pattern 'tx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, r: 1, y: 1, c: 3} to form a word, what is the expected number of matches of the pattern 'ro*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 3, g: 3} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, l: 2, y: 2}, what is the expected number of times the pattern 'y*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, m: 1, q: 1, j: 2, t: 1}, what is the expected number of times the pattern 'm+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, f: 1, n: 2, e: 1, w: 1}, what is the expected number of times the pattern 'wf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 5, d: 1}, what is the expected number of times the pattern 'c.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, w: 1, j: 1, p: 1, z: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 4, m: 2}, what is the expected number of times the pattern 'h.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, n: 2, k: 1, w: 1}, what is the expected number of times the pattern 'w*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, n: 1, q: 2, e: 2} to form a word, what is the expected number of matches of the pattern 'qn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, f: 4}. What is the expected number of occurrences of the pattern 'tf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, c: 1, i: 1, v: 1, u: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 4, l: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'zm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 2, t: 1, y: 3}. What is the expected number of occurrences of the pattern 'yx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, f: 3}, what is the expected number of times the pattern 'fo+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, h: 3}, what is the expected number of times the pattern 'h.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, l: 1, i: 1, p: 1, r: 1}. What is the expected number of occurrences of the pattern 'l+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, v: 2, b: 1, g: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'gr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, b: 1, j: 1, e: 2}. What is the expected number of occurrences of the pattern 's+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, c: 1, h: 2, y: 1, d: 1}, what is the expected number of times the pattern 'q*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, t: 1, m: 1, v: 2} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, c: 1, f: 2, l: 1, x: 1}, what is the expected number of times the pattern 'l+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, z: 1, b: 4}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, d: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, b: 1, t: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 3, f: 3} to form a word, what is the expected number of matches of the pattern 'd+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, y: 2, s: 1}. What is the expected number of occurrences of the pattern 'sz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, p: 2, m: 1}. What is the expected number of occurrences of the pattern 'r.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, y: 1, i: 1, c: 2, n: 1}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, a: 3, m: 2}, what is the expected number of times the pattern 'a.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, n: 2, v: 1, i: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, v: 2, c: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 4, o: 2}, what is the expected number of times the pattern 'do+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, g: 1, x: 1, z: 2, a: 1}, what is the expected number of times the pattern 'ax*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, i: 2, s: 2}, what is the expected number of times the pattern 'i.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 4, x: 2}, what is the expected number of times the pattern 'x.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, d: 1, z: 2, r: 1, b: 1}. What is the expected number of occurrences of the pattern 'd*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, s: 1, i: 1, g: 3}, what is the expected number of times the pattern 'i+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, c: 2, n: 1, s: 2}, what is the expected number of times the pattern 'nc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 2, l: 1, e: 3}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, i: 1, p: 1, z: 3}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 4, k: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, m: 1, q: 2, a: 1}, what is the expected number of times the pattern 'r*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, j: 2, m: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, i: 1, z: 1, h: 1, b: 1}. What is the expected number of occurrences of the pattern 'c*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, z: 1, g: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, y: 2, h: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, l: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'm.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, c: 2, f: 2}. What is the expected number of occurrences of the pattern 'ac+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, y: 1, u: 3} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, c: 4}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, m: 1, o: 3, e: 1}. What is the expected number of occurrences of the pattern 'o+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 2, i: 4} to form a word, what is the expected number of matches of the pattern 'it*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, q: 3}. What is the expected number of occurrences of the pattern 'qi+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 4, v: 2}, what is the expected number of times the pattern 'd.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, a: 1, u: 2, q: 2}. What is the expected number of occurrences of the pattern 'q+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 3, c: 3}. What is the expected number of occurrences of the pattern 'cn+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, b: 3}. What is the expected number of occurrences of the pattern 'pp+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 4, k: 2}. What is the expected number of occurrences of the pattern 'kr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 2, n: 4} to form a word, what is the expected number of matches of the pattern 'gn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, y: 1, g: 2}. What is the expected number of occurrences of the pattern 'rg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 3, f: 1, s: 2}, what is the expected number of times the pattern 's+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 5, w: 1} to form a word, what is the expected number of matches of the pattern 'w.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, z: 2, k: 1, v: 1, o: 1}, what is the expected number of times the pattern 'k.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, x: 4}, what is the expected number of times the pattern 'kx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 4, x: 2} to form a word, what is the expected number of matches of the pattern 'x.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, a: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, o: 1, a: 2, u: 2}. What is the expected number of occurrences of the pattern 'h+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, h: 2, n: 1, y: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'n+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, y: 2, s: 2}, what is the expected number of times the pattern 'zy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, i: 1, w: 1, e: 1, o: 1}, what is the expected number of times the pattern 'wm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, d: 2, b: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, b: 2, h: 2}, what is the expected number of times the pattern 't*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, p: 1, c: 2}. What is the expected number of occurrences of the pattern 'i*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, t: 3}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, z: 2, y: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'pz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, t: 1, y: 4}, what is the expected number of times the pattern 'ty+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, s: 2, y: 2} to form a word, what is the expected number of matches of the pattern 's.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, o: 1, e: 1, g: 3}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, x: 3, d: 2} to form a word, what is the expected number of matches of the pattern 'xd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 3, t: 3} to form a word, what is the expected number of matches of the pattern 'wt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, y: 2, f: 1, u: 1}, what is the expected number of times the pattern 'y*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, k: 1, i: 2, r: 1, d: 1}. What is the expected number of occurrences of the pattern 'r.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, m: 1, d: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, i: 2, x: 1, f: 1, m: 1}. What is the expected number of occurrences of the pattern 'xf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, x: 3}, what is the expected number of times the pattern 'rx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, y: 1, r: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'mr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, o: 2, w: 2, b: 1}, what is the expected number of times the pattern 'go*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, z: 2, d: 2, b: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, i: 2, x: 2}. What is the expected number of occurrences of the pattern 'x*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, b: 1, r: 1, v: 1, d: 2}, what is the expected number of times the pattern 'rb+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, i: 4} to form a word, what is the expected number of matches of the pattern 'm.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, k: 2, q: 1, f: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'uh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, v: 2, t: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'vm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, u: 2, a: 1, q: 2}, what is the expected number of times the pattern 'q+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, z: 1, o: 2, u: 2}. What is the expected number of occurrences of the pattern 'u+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, x: 1, y: 1, z: 1, w: 2}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, v: 2, p: 1, g: 2}. What is the expected number of occurrences of the pattern 'p+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, x: 1, m: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, n: 1, u: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'jn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, f: 1, o: 1, x: 1, e: 1}, what is the expected number of times the pattern 'oe*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, e: 2, p: 3}. What is the expected number of occurrences of the pattern 'p*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, f: 3}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, p: 3} to form a word, what is the expected number of matches of the pattern 'i+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, j: 1, w: 1, d: 3}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, t: 5}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, x: 2, f: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, e: 1, b: 3, s: 1}. What is the expected number of occurrences of the pattern 'n+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, a: 1, f: 1, d: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'ad+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, q: 1, o: 2, a: 1, f: 1}, what is the expected number of times the pattern 'v+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, l: 2, v: 1, h: 1, g: 1}. What is the expected number of occurrences of the pattern 'g.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, y: 1, l: 1, r: 1, g: 2}. What is the expected number of occurrences of the pattern 'lj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, d: 2, e: 1, v: 1, a: 1}. What is the expected number of occurrences of the pattern 've*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, s: 3}. What is the expected number of occurrences of the pattern 's+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, p: 3, t: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, y: 4}, what is the expected number of times the pattern 'xy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 4, t: 2}. What is the expected number of occurrences of the pattern 't+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 2, j: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, h: 2, r: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, g: 3}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, z: 3, p: 1}. What is the expected number of occurrences of the pattern 'pz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, d: 2, p: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'd*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, o: 1, l: 1, g: 1, a: 2}, what is the expected number of times the pattern 'l.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, r: 2, x: 2}, what is the expected number of times the pattern 'r*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 3, r: 3} to form a word, what is the expected number of matches of the pattern 'gr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, e: 4}. What is the expected number of occurrences of the pattern 'eb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, t: 1, y: 1, q: 1, l: 1}, what is the expected number of times the pattern 'o+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, a: 1, w: 2}. What is the expected number of occurrences of the pattern 'a*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, f: 1, e: 2, l: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, f: 3}. What is the expected number of occurrences of the pattern 'of*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, m: 1, l: 1, n: 1, r: 1}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 2, x: 1, b: 3}. What is the expected number of occurrences of the pattern 'xb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, t: 1, a: 1, f: 2, p: 1}, what is the expected number of times the pattern 'f+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, e: 1, z: 1, o: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'w+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, p: 1, e: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'f+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, z: 1, w: 2, c: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, z: 5} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, j: 3}, what is the expected number of times the pattern 'j*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, r: 1, g: 1, v: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, v: 2, i: 2, d: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, v: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'vb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, r: 1, v: 1, f: 2, j: 1}. What is the expected number of occurrences of the pattern 'kr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, p: 1, f: 1, h: 2}, what is the expected number of times the pattern 'h+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 3, p: 2, r: 1}. What is the expected number of occurrences of the pattern 't+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, c: 2}, what is the expected number of times the pattern 'cu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 5, c: 1}, what is the expected number of times the pattern 'cp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, q: 1, n: 1, e: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'd*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, v: 1, m: 1, w: 1, c: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, r: 5} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, l: 1, c: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'a+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, k: 3}, what is the expected number of times the pattern 'ok*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, q: 1, s: 1, o: 1, z: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, d: 1, y: 1, a: 3}, what is the expected number of times the pattern 'at+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, t: 1, n: 2, x: 1}, what is the expected number of times the pattern 'nx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, h: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, s: 1, e: 1, r: 1, i: 1}. What is the expected number of occurrences of the pattern 'se+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, z: 3}. What is the expected number of occurrences of the pattern 'oz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 3, g: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'dr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 4, k: 2}. What is the expected number of occurrences of the pattern 'kd+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, x: 2, m: 2, b: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, w: 2, z: 3}. What is the expected number of occurrences of the pattern 'zw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, r: 1, j: 2, o: 2}. What is the expected number of occurrences of the pattern 'o+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, u: 1, v: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, d: 2, a: 1, p: 2}, what is the expected number of times the pattern 'd*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, b: 1, z: 2, n: 1, g: 1}, what is the expected number of times the pattern 'qb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, r: 1, w: 1, j: 1, l: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, a: 1, e: 2, z: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'z.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, c: 1, i: 1, h: 1, q: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, r: 1, s: 1, j: 1, v: 1}, what is the expected number of times the pattern 'v.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, x: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'cp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, w: 2, a: 1, r: 1}, what is the expected number of times the pattern 'wd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, y: 4}, what is the expected number of times the pattern 'j.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, a: 3, y: 1}, what is the expected number of times the pattern 'c.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, q: 1, t: 2, f: 1}. What is the expected number of occurrences of the pattern 'i.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, b: 1, r: 2}, what is the expected number of times the pattern 'r.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 4, z: 2}. What is the expected number of occurrences of the pattern 'f.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, u: 2, v: 1, y: 2}. What is the expected number of occurrences of the pattern 'v+u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, y: 1, n: 2}. What is the expected number of occurrences of the pattern 'y.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, s: 2, n: 2, e: 1}, what is the expected number of times the pattern 'yn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, a: 2, d: 2}. What is the expected number of occurrences of the pattern 'ga+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {w: 1, t: 1, g: 1, z: 3} to form a word, what is the expected number of matches of the pattern 'g+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, s: 1, j: 2, z: 1}, what is the expected number of times the pattern 'rs*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, z: 1, t: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, t: 3} to form a word, what is the expected number of matches of the pattern 'a.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, o: 3}. What is the expected number of occurrences of the pattern 'oc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, a: 5}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, x: 1, i: 1, y: 2, p: 1}. What is the expected number of occurrences of the pattern 'ip+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, i: 2, k: 2}, what is the expected number of times the pattern 'tk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, n: 2, t: 1, w: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'c*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, y: 1, r: 2, h: 1, t: 1}, what is the expected number of times the pattern 'lt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'x+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, q: 1, p: 2, d: 1, j: 1}. What is the expected number of occurrences of the pattern 'j.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 5, g: 1} to form a word, what is the expected number of matches of the pattern 'gz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, n: 4}, what is the expected number of times the pattern 'na+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, q: 2, u: 2}, what is the expected number of times the pattern 'q.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, k: 3, l: 2} to form a word, what is the expected number of matches of the pattern 'k+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 2, k: 1, e: 1, o: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'h+q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, y: 3}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, o: 2, l: 1, a: 1, b: 1}. What is the expected number of occurrences of the pattern 'll+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, d: 1, i: 1, e: 1, u: 1}, what is the expected number of times the pattern 'ri+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, p: 2, m: 3}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, g: 1, i: 1, o: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'gi*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, e: 1, s: 1, h: 2} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, o: 3, u: 1}. What is the expected number of occurrences of the pattern 'f+o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, h: 5} to form a word, what is the expected number of matches of the pattern 'n.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 4, j: 2}. What is the expected number of occurrences of the pattern 'mj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, q: 2, j: 2, e: 1}. What is the expected number of occurrences of the pattern 'e*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, h: 4}. What is the expected number of occurrences of the pattern 'n+h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, x: 2, r: 2}, what is the expected number of times the pattern 'ra+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, g: 2, v: 1}, what is the expected number of times the pattern 'g+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, q: 1, g: 2, d: 1, c: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 4, b: 2}, what is the expected number of times the pattern 'p*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, y: 5}, what is the expected number of times the pattern 'r+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, f: 3, y: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'g+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 3, k: 3} to form a word, what is the expected number of matches of the pattern 'e.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, r: 1, d: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, w: 1, n: 1, z: 1, x: 1}, what is the expected number of times the pattern 'wx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, v: 1, i: 1, k: 1, p: 2}, what is the expected number of times the pattern 'ai+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, m: 1, u: 3, f: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, m: 4}. What is the expected number of occurrences of the pattern 't.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, y: 2, j: 2, p: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, q: 3}, what is the expected number of times the pattern 'qd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, w: 5}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 4, y: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 4, f: 2} to form a word, what is the expected number of matches of the pattern 'fm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.73", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, v: 1, d: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 3, s: 3} to form a word, what is the expected number of matches of the pattern 's+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, c: 2, g: 1, d: 1, u: 1}, what is the expected number of times the pattern 'j.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, h: 1, x: 4}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, a: 3} to form a word, what is the expected number of matches of the pattern 'a.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, h: 2, y: 1}, what is the expected number of times the pattern 'y+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 2, w: 4} to form a word, what is the expected number of matches of the pattern 'w.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, g: 2, z: 1, a: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, r: 1, z: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'rz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, a: 1, c: 3}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, x: 4}, what is the expected number of times the pattern 'rx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, p: 1, h: 2, j: 1, d: 1}, what is the expected number of times the pattern 'l.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, o: 2, j: 2, b: 1}, what is the expected number of times the pattern 'o.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, t: 2, s: 1, a: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 1, l: 1, y: 3, v: 1} to form a word, what is the expected number of matches of the pattern 'ul*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 5, j: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 4, b: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 3, c: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'fc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, k: 1, w: 2, q: 1, e: 1}. What is the expected number of occurrences of the pattern 'g*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 3, m: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'iv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.95", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, x: 1, k: 1, o: 3} to form a word, what is the expected number of matches of the pattern 'x+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, s: 4} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, w: 1, x: 2, y: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'xy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, r: 1, x: 3}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, h: 2, i: 1, r: 1, z: 1}. What is the expected number of occurrences of the pattern 'rz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, q: 1, j: 1, b: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, r: 1, c: 1, k: 1, i: 1}, what is the expected number of times the pattern 'rk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, f: 2, q: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'f+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, a: 1, h: 1, k: 2, u: 1}. What is the expected number of occurrences of the pattern 'h+a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, u: 1, x: 2, l: 2}. What is the expected number of occurrences of the pattern 'u+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, x: 1, v: 1, a: 1}. What is the expected number of occurrences of the pattern 'xa*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, f: 1, z: 2, j: 1, b: 1}, what is the expected number of times the pattern 'j.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, t: 3}. What is the expected number of occurrences of the pattern 'tc+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, y: 1, a: 2, q: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'z.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, e: 2, x: 1, b: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, m: 2, z: 1}. What is the expected number of occurrences of the pattern 'j.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, g: 1, b: 1, l: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, l: 2, d: 1, v: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, p: 1, e: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'u+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 3, k: 3} to form a word, what is the expected number of matches of the pattern 'k.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, v: 1, z: 3}, what is the expected number of times the pattern 'vz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, f: 3}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, m: 3, j: 1}. What is the expected number of occurrences of the pattern 'j*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, v: 1, u: 1, t: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 4, p: 2} to form a word, what is the expected number of matches of the pattern 'kp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, u: 2, s: 1, t: 2}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, f: 1, d: 1, o: 2, i: 1}, what is the expected number of times the pattern 'di+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, y: 1, u: 2, c: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, m: 2, v: 1, e: 1}, what is the expected number of times the pattern 't+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 3, m: 3}. What is the expected number of occurrences of the pattern 'ms+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, t: 3, o: 2}, what is the expected number of times the pattern 'g*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, r: 1, q: 1, a: 2, o: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'vr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, s: 1, r: 1, z: 2}. What is the expected number of occurrences of the pattern 'rz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, r: 2, d: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'j.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, s: 2, g: 1, a: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'a*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, i: 1, t: 1, n: 1, p: 2}, what is the expected number of times the pattern 'm.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, b: 1, i: 1, s: 1, z: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, m: 2, w: 2, c: 1}. What is the expected number of occurrences of the pattern 'mq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, q: 1, t: 2, f: 2} to form a word, what is the expected number of matches of the pattern 'q.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, w: 1, y: 1, b: 2, s: 1}, what is the expected number of times the pattern 'sb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, s: 1, q: 1, r: 3} to form a word, what is the expected number of matches of the pattern 'ps+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, z: 1, s: 2}. What is the expected number of occurrences of the pattern 'z*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 3, r: 1, v: 2}. What is the expected number of occurrences of the pattern 'rv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, f: 4, b: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'h*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, x: 1, m: 3} to form a word, what is the expected number of matches of the pattern 'm+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, w: 1, o: 2, m: 1, n: 1}, what is the expected number of times the pattern 'wn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, w: 1, j: 2}. What is the expected number of occurrences of the pattern 'y*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, b: 2, t: 1, v: 2}. What is the expected number of occurrences of the pattern 'vb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, a: 3, o: 2} to form a word, what is the expected number of matches of the pattern 'y*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, h: 4} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, c: 1, r: 2, i: 1, v: 1}, what is the expected number of times the pattern 'rv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, y: 3}. What is the expected number of occurrences of the pattern 'o+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, k: 1, l: 2, g: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, k: 1, t: 2, l: 2}, what is the expected number of times the pattern 'll*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, s: 2, e: 2, o: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, q: 1, s: 4}. What is the expected number of occurrences of the pattern 'sq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.27", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, q: 1, t: 2, f: 1, l: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, i: 1, k: 1, y: 1, t: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, s: 1, z: 1, l: 2, r: 1}, what is the expected number of times the pattern 'kz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, b: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, g: 1, x: 3}, what is the expected number of times the pattern 'gr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, l: 1, r: 2, j: 1, y: 1}, what is the expected number of times the pattern 'dl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, w: 5}. What is the expected number of occurrences of the pattern 'i.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, e: 2, y: 1, p: 1, o: 1}, what is the expected number of times the pattern 'o*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, g: 2, q: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'gv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, v: 2, m: 2, i: 1}, what is the expected number of times the pattern 'mr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 5, h: 1}, what is the expected number of times the pattern 'hs*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, f: 3}. What is the expected number of occurrences of the pattern 'f.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, m: 1, b: 1, p: 1}. What is the expected number of occurrences of the pattern 'd.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 2, d: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'e*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 3, j: 1, m: 2}, what is the expected number of times the pattern 'p+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, z: 1, h: 1, e: 1, p: 2}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, i: 3, m: 2} to form a word, what is the expected number of matches of the pattern 'ma*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, h: 3}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, h: 1, o: 2, v: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, b: 1, t: 1, m: 2, v: 1}. What is the expected number of occurrences of the pattern 'vd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, t: 1, g: 1, k: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, z: 2, t: 1, r: 1, y: 1}, what is the expected number of times the pattern 't.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, x: 3, f: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'v+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, a: 2, j: 2}. What is the expected number of occurrences of the pattern 'aj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, o: 4}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, k: 2, e: 2, z: 1}, what is the expected number of times the pattern 'ke*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, b: 3, v: 2}, what is the expected number of times the pattern 'vv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, n: 2}. What is the expected number of occurrences of the pattern 'n.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, b: 3}. What is the expected number of occurrences of the pattern 'fb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, l: 1, q: 3, n: 1}, what is the expected number of times the pattern 'nq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, y: 1, l: 1, m: 2, z: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, c: 2, v: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'c+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, e: 1, n: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, p: 3, b: 1, v: 1}. What is the expected number of occurrences of the pattern 'l*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 2, p: 2, f: 2} to form a word, what is the expected number of matches of the pattern 'po*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, n: 3, h: 2} to form a word, what is the expected number of matches of the pattern 'hc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, y: 1, n: 2, j: 1}. What is the expected number of occurrences of the pattern 'n.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, s: 1, c: 1, n: 2}. What is the expected number of occurrences of the pattern 'c*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, s: 2, p: 1, t: 1}. What is the expected number of occurrences of the pattern 't+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, q: 2, o: 1, h: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, w: 2, h: 2, f: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, c: 2, x: 2}. What is the expected number of occurrences of the pattern 'cl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 1, c: 1, o: 1, y: 2, n: 1}, what is the expected number of times the pattern 'on*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, m: 3, j: 2}, what is the expected number of times the pattern 'ju+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, u: 1, d: 2, a: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'vu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, u: 1, e: 2, h: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 5, y: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, w: 2, v: 1, z: 1}. What is the expected number of occurrences of the pattern 'rv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, g: 2, l: 3}, what is the expected number of times the pattern 'g+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, x: 3}, what is the expected number of times the pattern 'x.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, x: 1, c: 2, r: 1, z: 1}, what is the expected number of times the pattern 'mc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, p: 2, l: 1, x: 2}, what is the expected number of times the pattern 'xp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, d: 1, s: 1, t: 1, m: 2}. What is the expected number of occurrences of the pattern 's+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 4, a: 1, z: 1}, what is the expected number of times the pattern 'a.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, n: 4} to form a word, what is the expected number of matches of the pattern 'a+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, u: 2, h: 1, n: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'n+u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, b: 3, r: 1}, what is the expected number of times the pattern 'r+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, d: 1, x: 1, t: 1, v: 1}, what is the expected number of times the pattern 'x*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, c: 1, u: 1, i: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'uz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 3, l: 2, k: 1}. What is the expected number of occurrences of the pattern 'kl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 4, w: 2} to form a word, what is the expected number of matches of the pattern 'e.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}