diff --git "a/data.jsonl" "b/data.jsonl"
new file mode 100644--- /dev/null
+++ "b/data.jsonl"
@@ -0,0 +1,1000 @@
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {s: 1, x: 1, t: 1, i: 1}. What is the expected number of occurrences of the pattern 's.*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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {f: 1, m: 3, j: 2}. 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 1, z: 1, c: 1, n: 1}, what is the expected number of times the pattern 'z.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, v: 1, c: 1, q: 1}. What is the expected number of occurrences of the pattern 'c.*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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, j: 2}. What is the expected number of occurrences of the pattern 'r+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": "0.83", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, f: 2, b: 1, e: 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 2 letters from the multiset {m: 1, q: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'qf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 3, g: 2}, what is the expected number of times the pattern 'cg+' 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 2 letters from the multiset {b: 3, h: 2}. What is the expected number of occurrences of the pattern 'h*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": "1.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {y: 1, l: 2, v: 2}. 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": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, j: 1, d: 2, e: 1}. What is the expected number of occurrences of the pattern 'qd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.83", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 1, n: 1, a: 1, k: 1, c: 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 {c: 3, 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": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, u: 1, y: 1}, what is the expected number of times the pattern 'ut*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, z: 3, l: 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": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, y: 2, k: 3}. 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": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 1, o: 2, g: 1}, what is the expected number of times the pattern 'f*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, x: 2, r: 1, a: 1}, 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": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {a: 3, f: 3} to form a word, what is the expected number of matches of the pattern 'f.*a'? 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 2 letters from the multiset {t: 1, d: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'd.*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 2 by randomly selecting letters from the multiset {n: 1, s: 1, l: 1, g: 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 {h: 4, i: 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": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {t: 2, x: 2} 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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, o: 1, e: 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": "If you form a word of length 2 by randomly selecting letters from the multiset {j: 2, s: 2}, what is the expected number of times the pattern 'j+s' 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": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 1, d: 2, w: 1, b: 1}, 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, b: 4} to form a word, what is the expected number of matches of the pattern 'fb+'? 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 {y: 1, s: 1, o: 2, d: 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": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, b: 1, f: 1, a: 1, d: 1}, what is the expected number of times the pattern 'df+' 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 {u: 2, s: 2, z: 1, h: 1}, what is the expected number of times the pattern 'uz*' 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 2 by randomly selecting letters from the multiset {e: 3, y: 3}, what is the expected number of times the pattern 'ye+' 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 {v: 1, m: 1, h: 2, a: 1}. What is the expected number of occurrences of the pattern 'v.*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": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 2, j: 4}, what is the expected number of times the pattern 'jh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, k: 1, b: 1, x: 3}. What is the expected number of occurrences of the pattern 'a*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": "Form a word by randomly choosing 3 letters from the multiset {l: 1, u: 2, e: 2}. What is the expected number of occurrences of the pattern 'e.*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": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 1, g: 2, i: 2, r: 1}, 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": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, l: 2, h: 1, f: 1, c: 1}. What is the expected number of occurrences of the pattern 'f.*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": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, d: 2, l: 1, r: 1, y: 1}, what is the expected number of times the pattern 'd.*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": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 1, w: 3, g: 1}, what is the expected number of times the pattern 'g*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.35", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, c: 1, p: 2, q: 1}, 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, l: 1, i: 1, x: 1}, what is the expected number of times the pattern 'i+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {v: 1, l: 2, g: 1} 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": "0.67", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, i: 1, c: 1, g: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? 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 2 letters from the multiset {l: 4, q: 1} 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": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 1, z: 1, c: 1, n: 1, x: 1}, what is the expected number of times the pattern 'cz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {l: 4, x: 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": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, p: 1, u: 1, a: 1, 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 2 letters from the multiset {c: 1, n: 3} 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {w: 1, u: 2, p: 2}. What is the expected number of occurrences of the pattern 'pw*' in 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 {k: 1, x: 3, r: 1, l: 1}, what is the expected number of times the pattern 'k+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 2 letters from the multiset {v: 1, k: 3} to form a word, what is the expected number of matches of the pattern 'k*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": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 1, m: 1, j: 2}, what is the expected number of times the pattern 'r.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 2, s: 1, y: 2}, what is the expected number of times the pattern 's.*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": "When randomly selecting 2 letters from the multiset {k: 1, w: 2, o: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'w*k'? 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 2 letters from the multiset {r: 1, n: 2, w: 2, t: 1}. What is the expected number of occurrences of the pattern 'tw+' in 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 2 by randomly selecting letters from the multiset {g: 1, r: 1, q: 1, t: 1}, what is the expected number of times the pattern 'tg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 1, c: 2, z: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'm*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {w: 1, b: 1, c: 1, u: 1} 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {o: 1, p: 1, r: 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 2 by randomly selecting letters from the multiset {q: 2, y: 3}, what is the expected number of times the pattern 'yq+' 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 2 by randomly selecting letters from the multiset {r: 1, b: 4}, 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 {c: 1, r: 1, t: 2, q: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'c*j'? 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 2 letters from the multiset {k: 3, u: 2} to form a word, what is the expected number of matches of the pattern 'k*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 2, b: 3}, what is the expected number of times the pattern 'eb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {u: 4, n: 2}. What is the expected number of occurrences of the pattern 'n+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": "0.27", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {i: 2, r: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'rt*'? 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 2 letters from the multiset {a: 2, g: 3, u: 1} 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 1, b: 3} 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": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 1, l: 3, u: 1, a: 1}, what is the expected number of times the pattern 'u*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {e: 1, o: 1, q: 1, k: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, x: 1, j: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'g+j'? 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, z: 1, w: 2, j: 1, d: 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": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 1, z: 1, s: 2}, what is the expected number of times the pattern 'es+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, k: 3, t: 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": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {q: 1, k: 1, p: 1, g: 1, w: 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": "When randomly selecting 2 letters from the multiset {k: 2, d: 3} to form a word, what is the expected number of matches of the pattern 'kd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {c: 1, v: 1, h: 1, g: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'g*h'? 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 2 letters from the multiset {g: 3, z: 3}. What is the expected number of occurrences of the pattern 'g*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": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 2, e: 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": "2.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, e: 1, d: 2, h: 1}. What is the expected number of occurrences of the pattern 'h*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": "When randomly selecting 2 letters from the multiset {l: 2, x: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'al+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {z: 1, a: 2, n: 1}. What is the expected number of occurrences of the pattern 'zn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 2, c: 3} to form a word, what is the expected number of matches of the pattern 'c.*j'? 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: 3, x: 1, t: 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": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 2, t: 2, r: 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": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, w: 1, s: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {z: 4, h: 1}, what is the expected number of times the pattern 'z+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 {q: 4, u: 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": "1.8", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, u: 1}, what is the expected number of times the pattern 'zu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'yd+'? 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: 1, b: 2, m: 1, z: 1}. What is the expected number of occurrences of the pattern 'm.*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": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, n: 2}, what is the expected number of times the pattern 'z.*n' 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 2 by randomly selecting letters from the multiset {c: 1, s: 1, v: 1, o: 1, z: 1}, what is the expected number of times the pattern 's.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, j: 1, k: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'k.*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": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, w: 1, j: 1, f: 1, y: 1}, what is the expected number of times the pattern 'jy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {j: 1, e: 1, c: 1, t: 1, b: 1}, what is the expected number of times the pattern 't.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {q: 3, t: 1} 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 2 by randomly selecting letters from the multiset {q: 1, n: 1, t: 1, l: 1, o: 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": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, y: 1, w: 1, a: 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": "0.92", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {x: 1, t: 1, h: 2, o: 1}. What is the expected number of occurrences of the pattern 'h+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": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, g: 1, q: 1, l: 1}, what is the expected number of times the pattern 'k*q' 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 2 letters from the multiset {p: 1, l: 1, r: 1, 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 {b: 1, q: 1, n: 1, l: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'f*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {q: 1, o: 1, b: 1, d: 1, n: 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": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 2, w: 3}, what is the expected number of times the pattern 'w+q' 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 2 letters from the multiset {t: 2, l: 1, r: 1, f: 1, q: 1}. What is the expected number of occurrences of the pattern 'rt+' in 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 2 by randomly selecting letters from the multiset {k: 1, x: 1, g: 2, l: 1}, what is the expected number of times the pattern 'x*k' 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 {s: 1, t: 1, p: 1, g: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'n+p'? 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 {n: 4, a: 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": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, o: 1}, what is the expected number of times the pattern 'z.*o' 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 {l: 1, g: 1, m: 1, e: 1, u: 1}, 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": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 1, d: 1, g: 1, k: 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 2 by randomly selecting letters from the multiset {h: 2, o: 3, t: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, f: 1, m: 1, n: 1, q: 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": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 1, w: 3, f: 1}, what is the expected number of times the pattern 'w.*m' 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 2 by randomly selecting letters from the multiset {d: 3, 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": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {x: 1, v: 1, g: 1, l: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, h: 1, x: 1, j: 1, s: 1}. What is the expected number of occurrences of the pattern 'j+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": "Form a word by randomly choosing 3 letters from the multiset {g: 3, e: 3}. What is the expected number of occurrences of the pattern 'g.*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": "When randomly selecting 3 letters from the multiset {o: 1, w: 2, t: 1, l: 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": "Form a word by randomly choosing 2 letters from the multiset {l: 2, u: 1, c: 1, z: 1}. What is the expected number of occurrences of the pattern 'z+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": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, e: 1, m: 1, b: 1, h: 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 {d: 1, k: 1, o: 1, s: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'dk+'? 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 2 letters from the multiset {f: 2, k: 4}. What is the expected number of occurrences of the pattern 'kf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, f: 1, e: 1, q: 2} 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": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 1, w: 2, y: 1}, what is the expected number of times the pattern 'w*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {c: 1, v: 2, u: 1} 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, g: 1, p: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'd.*p'? 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 2 by randomly selecting letters from the multiset {e: 1, t: 1, z: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {m: 2, n: 2}. What is the expected number of occurrences of the pattern 'm+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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {s: 1, c: 1, l: 2} to form a word, what is the expected number of matches of the pattern 's*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, r: 1, i: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, q: 3, 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": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, d: 3}, what is the expected number of times the pattern 'd*z' 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 {l: 1, v: 2, i: 1}. What is the expected number of occurrences of the pattern 'vi+' in 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": "When randomly selecting 3 letters from the multiset {j: 2, h: 3} to form a word, what is the expected number of matches of the pattern 'hj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, n: 1, d: 1}. What is the expected number of occurrences of the pattern 'o.*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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {s: 2, f: 1, z: 2} 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, j: 1, w: 1, o: 1, y: 2}. What is the expected number of occurrences of the pattern 'y.*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": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, t: 1, n: 1, g: 1}, what is the expected number of times the pattern 'g*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.92", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 2, x: 1, d: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 1, j: 2, q: 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": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 3, t: 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": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {y: 1, l: 1, t: 1, f: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 1, e: 2, v: 3}, what is the expected number of times the pattern 'v+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 {f: 2, g: 3, l: 1}. What is the expected number of occurrences of the pattern 'fg+' in 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 {v: 1, z: 1, a: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'az+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 1, w: 1, f: 1, v: 1, z: 1}, 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": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 1, x: 1, j: 1, r: 1}, what is the expected number of times the pattern 'fr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {j: 1, k: 3, v: 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": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, c: 4}. What is the expected number of occurrences of the pattern 'c+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": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, k: 2, i: 1, t: 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": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {y: 1, f: 2, s: 1, k: 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": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, q: 1, l: 2, h: 1}, 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": "When randomly selecting 3 letters from the multiset {h: 2, s: 1, u: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'u+j'? 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 {g: 1, q: 1, h: 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": "0.92", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {j: 2, y: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'j.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, x: 3} to form a word, what is the expected number of matches of the pattern 'x.*h'? 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 2 letters from the multiset {e: 1, l: 1, a: 1, q: 2, i: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {g: 1, p: 5}. 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": "0.67", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, c: 3}. What is the expected number of occurrences of the pattern 'c.*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": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {q: 1, c: 2, r: 1, p: 1, n: 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": "Form a word by randomly choosing 3 letters from the multiset {e: 2, o: 1, j: 1, q: 2}. 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 {u: 2, z: 1, b: 1, j: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'zb+'? 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 2 letters from the multiset {p: 1, i: 3, v: 2} to form a word, what is the expected number of matches of the pattern 'p+i'? 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 2 letters from the multiset {i: 1, y: 1, g: 1, k: 1}. What is the expected number of occurrences of the pattern 'iy*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {d: 1, j: 2, g: 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": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {a: 4, y: 2}. What is the expected number of occurrences of the pattern 'y+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": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {h: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'h+y'? 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": "Form a word by randomly choosing 2 letters from the multiset {k: 1, o: 1, c: 1, x: 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": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 3, f: 3}, what is the expected number of times the pattern 's*f' 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 {c: 1, z: 1, q: 1, f: 2, d: 1}, 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": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 2, n: 2, l: 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": "Form a word by randomly choosing 3 letters from the multiset {r: 1, p: 2, e: 1, z: 2}. 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": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {g: 2, x: 4} 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": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {v: 2, w: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'aw*'? 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: 1, u: 1, q: 1, c: 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": "Form a word by randomly choosing 3 letters from the multiset {h: 1, a: 4}. 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 {u: 1, y: 3}, 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": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, o: 2, a: 3}. 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": "1.7", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, s: 2, l: 1}, 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": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, n: 1, o: 1, b: 1, q: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {b: 1, l: 1, i: 2, f: 2}. What is the expected number of occurrences of the pattern 'i*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": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, r: 1, l: 1, w: 1}. What is the expected number of occurrences of the pattern 'dr+' in 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 {k: 1, j: 2, l: 3} to form a word, what is the expected number of matches of the pattern 'l.*k'? 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 2 letters from the multiset {k: 2, f: 2, g: 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": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {j: 2, e: 1, q: 1, s: 1, 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {z: 1, x: 1, v: 1, t: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'v*x'? 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 2 by randomly selecting letters from the multiset {y: 1, f: 4, n: 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": "0.37", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, d: 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": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {m: 2, f: 1, j: 1, n: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'ni+'? 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 2 letters from the multiset {y: 1, k: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'n.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 1, y: 1, j: 2, w: 2}, what is the expected number of times the pattern 'jc+' 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 2 letters from the multiset {p: 2, 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, j: 1, x: 1, c: 1, q: 1}, what is the expected number of times the pattern 'i*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {i: 1, v: 3}, what is the expected number of times the pattern 'i+v' 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": "If you form a word of length 2 by randomly selecting letters from the multiset {i: 1, a: 1, d: 2, l: 1}, what is the expected number of times the pattern 'li*' 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": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, s: 1, m: 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": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {w: 1, k: 1, h: 1, q: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'wq*'? 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 {x: 1, h: 3, s: 1, p: 1}, 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, m: 3, n: 1}, what is the expected number of times the pattern 'm+n' 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": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 1, q: 1, t: 1, j: 1}, what is the expected number of times the pattern 'hq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, p: 1, r: 1, f: 2}, what is the expected number of times the pattern 'p+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": "Form a word by randomly choosing 3 letters from the multiset {r: 1, h: 1, m: 1, n: 1}. What is the expected number of occurrences of the pattern 'm.*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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, h: 1, a: 2}. What is the expected number of occurrences of the pattern 'h+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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, w: 1, j: 2, z: 2}. 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": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, z: 2, k: 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": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, y: 2, x: 2}, 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": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {s: 4, r: 2} to form a word, what is the expected number of matches of the pattern 'rs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.93", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, x: 4}, 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": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {l: 3, y: 2} 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": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {r: 3, 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": "Form a word by randomly choosing 3 letters from the multiset {l: 1, u: 2, y: 1, p: 1}. 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": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 1, f: 3} to form a word, what is the expected number of matches of the pattern 'fx+'? 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: 4, q: 2} 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": "Form a word by randomly choosing 2 letters from the multiset {e: 2, 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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {d: 1, e: 2, i: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, m: 1, n: 1, t: 2, h: 1}. What is the expected number of occurrences of the pattern 'ht*' in 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 {p: 2, h: 3}. What is the expected number of occurrences of the pattern 'ph+' in 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 2 letters from the multiset {c: 3, y: 2}. What is the expected number of occurrences of the pattern 'yc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, p: 3}, what is the expected number of times the pattern 'p*g' 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 {j: 2, p: 4}. What is the expected number of occurrences of the pattern 'p+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": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {j: 2, t: 1, e: 2, x: 1}. What is the expected number of occurrences of the pattern 'je*' in 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 2 by randomly selecting letters from the multiset {k: 3, b: 1}, what is the expected number of times the pattern 'kk*' 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": "When randomly selecting 2 letters from the multiset {v: 1, u: 1, f: 2, b: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'v+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.03", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 2, c: 2, f: 1}, what is the expected number of times the pattern 'c.*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 2 letters from the multiset {c: 2, j: 1, i: 1, l: 1}. What is the expected number of occurrences of the pattern 'li+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, r: 1, o: 1, i: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'i.*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": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, w: 1, j: 2}, what is the expected number of times the pattern 'w.*s' 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": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, y: 1, i: 1, n: 1, v: 1}, what is the expected number of times the pattern 'y.*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": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 1, x: 2, a: 1, n: 1, z: 1}, what is the expected number of times the pattern 'xz+' 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 {r: 2, c: 1, t: 1, d: 1, b: 1}, what is the expected number of times the pattern 'cd*' 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 2 by randomly selecting letters from the multiset {f: 2, x: 3}, what is the expected number of times the pattern 'xf+' 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 2 letters from the multiset {v: 2, p: 1, d: 1, u: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'dv+'? 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 {t: 1, z: 2, s: 1, k: 1}, 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": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 4, l: 2}, what is the expected number of times the pattern 'ly*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.93", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, e: 1, n: 2, y: 1, h: 1}. What is the expected number of occurrences of the pattern 'x*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": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 3, k: 2}, 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": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, r: 2, f: 1, z: 1}, what is the expected number of times the pattern 'zh*' 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 2 letters from the multiset {l: 3, m: 1, w: 1}. What is the expected number of occurrences of the pattern 'l.*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": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, x: 1, h: 1, w: 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": "0.92", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, u: 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": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 1, a: 2, w: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'v*a'? 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 2 by randomly selecting letters from the multiset {c: 1, e: 1, p: 1, b: 1, r: 1}, what is the expected number of times the pattern 'p.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {f: 1, z: 1, w: 1, n: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'f.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 1, k: 3}, what is the expected number of times the pattern 'q.*k' 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 2 letters from the multiset {c: 1, s: 2, w: 1}. 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": "1.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, q: 2, h: 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": "1.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {h: 3, z: 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": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {t: 3, c: 1} to form a word, what is the expected number of matches of the pattern 't*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": "When randomly selecting 3 letters from the multiset {g: 1, f: 1, n: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'q*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.92", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 1, i: 4}, 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": "If you form a word of length 2 by randomly selecting letters from the multiset {a: 2, g: 2, z: 1, i: 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": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 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": "When randomly selecting 2 letters from the multiset {x: 1, d: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'd.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 4, o: 1}, what is the expected number of times the pattern 'o+p' 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 2 letters from the multiset {d: 1, r: 2, y: 2}. What is the expected number of occurrences of the pattern 'd*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": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, n: 1}. What is the expected number of occurrences of the pattern 'no*' 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 2 letters from the multiset {l: 3, f: 3}. What is the expected number of occurrences of the pattern 'fl*' 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 {n: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'xn*'? 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 {a: 1, m: 3, p: 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": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, c: 1, l: 2}, what is the expected number of times the pattern 'l+c' 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 2 letters from the multiset {a: 2, g: 1, e: 1, i: 1, t: 1} to form a word, what is the expected number of matches of the pattern 't*i'? 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 {r: 1, y: 1, d: 2, f: 1}. What is the expected number of occurrences of the pattern 'd.*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": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {p: 2, z: 1, h: 1, c: 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": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, r: 1, l: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'il+'? 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 {c: 1, z: 1, o: 1, n: 1, p: 2}. What is the expected number of occurrences of the pattern 'n+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": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 1, k: 1, y: 1, j: 1, s: 1}, what is the expected number of times the pattern 'vk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {d: 2, c: 1, h: 1, z: 2}. 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": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {j: 3, e: 3}. What is the expected number of occurrences of the pattern 'e.*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": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, z: 1, m: 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": "Form a word by randomly choosing 2 letters from the multiset {a: 2, b: 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": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, i: 2, d: 3} 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": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {p: 2, z: 1, y: 1, u: 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": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, n: 1, d: 1, p: 1, r: 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": "Form a word by randomly choosing 2 letters from the multiset {r: 1, l: 1, m: 1, t: 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 {n: 2, b: 1, l: 1, c: 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 {s: 1, c: 1, h: 1, g: 1, f: 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": "When randomly selecting 3 letters from the multiset {y: 2, e: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'y+e'? 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 {r: 2, f: 1, i: 2, o: 1} 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, j: 1, h: 1, t: 1, y: 1}, what is the expected number of times the pattern 'yq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {s: 2, 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": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 1, f: 2, u: 3}, what is the expected number of times the pattern 'f.*u' 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 2 by randomly selecting letters from the multiset {n: 1, h: 1, o: 1, s: 2, z: 1}, what is the expected number of times the pattern 'z*o' 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 {p: 1, z: 1, q: 2, 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": "Form a word by randomly choosing 3 letters from the multiset {m: 1, k: 1, 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {d: 1, s: 4}. 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": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {r: 2, c: 2, k: 1} 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": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 2, t: 1, j: 1}, what is the expected number of times the pattern 'j.*j' 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 2 letters from the multiset {l: 2, g: 1, y: 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": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {l: 1, n: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, b: 1, j: 1, l: 1}. 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": "If you form a word of length 2 by randomly selecting letters from the multiset {b: 1, c: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, r: 2}. What is the expected number of occurrences of the pattern 'rd*' 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 {r: 2, b: 3}. What is the expected number of occurrences of the pattern 'rr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, z: 1, x: 2}, what is the expected number of times the pattern 'x.*z' 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 {w: 2, q: 1, d: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, y: 1, h: 1, q: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 1, c: 1, a: 1, s: 2, j: 1}, what is the expected number of times the pattern 'j.*j' 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 {b: 2, j: 4}. What is the expected number of occurrences of the pattern 'jj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {e: 2, v: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'e.*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": "Form a word by randomly choosing 3 letters from the multiset {u: 2, v: 1, l: 3}. What is the expected number of occurrences of the pattern 'vu*' in 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 {t: 2, i: 2}, what is the expected number of times the pattern 'i*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {b: 1, a: 1, h: 1, w: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'na+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {k: 1, r: 2, n: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'nr*'? 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 {t: 2, m: 2, x: 2}, what is the expected number of times the pattern 'mt*' 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 2 by randomly selecting letters from the multiset {u: 4, x: 1, w: 1}, 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": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, t: 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": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, x: 1, b: 2, h: 1}. What is the expected number of occurrences of the pattern 'xo+' in 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 2 by randomly selecting letters from the multiset {x: 3, e: 2, p: 1}, what is the expected number of times the pattern 'p+e' 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 2 by randomly selecting letters from the multiset {b: 2, g: 1, k: 2, i: 1}, what is the expected number of times the pattern 'ib*' 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 2 by randomly selecting letters from the multiset {a: 2, s: 2, t: 1}, what is the expected number of times the pattern 't.*s' 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 {a: 2, n: 3} 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": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {y: 1, c: 1, i: 3}. 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 2 letters from the multiset {o: 1, v: 1, z: 1, g: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'go+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, a: 2}. What is the expected number of occurrences of the pattern 'va*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.33", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, m: 2}. 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {i: 1, x: 1, b: 1, u: 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": "When randomly selecting 3 letters from the multiset {a: 2, c: 4} to form a word, what is the expected number of matches of the pattern 'ca+'? 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 2 letters from the multiset {s: 2, d: 1, v: 1, i: 1, b: 1} to form a word, what is the expected number of matches of the pattern 's.*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 2 by randomly selecting letters from the multiset {y: 1, f: 1, w: 1, l: 1, o: 1}, 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": "0.45", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, p: 1, z: 1}, what is the expected number of times the pattern 'pz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.92", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {m: 2, z: 2, x: 1}. What is the expected number of occurrences of the pattern 'x.*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": "Form a word by randomly choosing 2 letters from the multiset {a: 1, k: 2, r: 1, d: 1}. What is the expected number of occurrences of the pattern 'd.*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": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {c: 2, l: 3} to form a word, what is the expected number of matches of the pattern 'l.*c'? 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 {v: 2, j: 2, r: 2} to form a word, what is the expected number of matches of the pattern 'jr+'? 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 2 letters from the multiset {s: 2, b: 1, x: 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 {n: 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 2 by randomly selecting letters from the multiset {a: 1, h: 1, w: 1, f: 1, 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 {e: 4, b: 1}, 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": "4.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {h: 1, j: 3, 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": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, w: 2, n: 1}. What is the expected number of occurrences of the pattern 'w+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": "0.42", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, r: 1, e: 1, f: 1, d: 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 {s: 1, k: 1, d: 2, v: 1, y: 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": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {l: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'l+y'? 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, i: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? 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 2 letters from the multiset {q: 3, f: 2}. 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": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, u: 2, s: 1}. What is the expected number of occurrences of the pattern 'u+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": "0.23", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {b: 1, c: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'cb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.92", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 1, t: 1, r: 1, w: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'c*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {z: 2, v: 3}, what is the expected number of times the pattern 'v*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, z: 3}. What is the expected number of occurrences of the pattern 'o+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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 1, m: 1, o: 2, r: 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 {m: 1, j: 5}, what is the expected number of times the pattern 'jm+' 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 2 letters from the multiset {u: 3, t: 2} to form a word, what is the expected number of matches of the pattern 'tu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {w: 1, o: 1, f: 3, a: 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 {o: 1, u: 1, k: 1, j: 1, w: 1}. 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": "0.7", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, z: 2}, what is the expected number of times the pattern 'z.*b' 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 2 letters from the multiset {j: 1, w: 1, k: 3}. What is the expected number of occurrences of the pattern 'k*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": "0.55", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {h: 2, o: 3, w: 1}. What is the expected number of occurrences of the pattern 'h.*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": "Form a word by randomly choosing 2 letters from the multiset {r: 1, k: 1, l: 1, v: 1, u: 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": "0.45", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {u: 1, h: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'zh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {l: 1, p: 1, s: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'ls*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {v: 1, o: 3, m: 2} 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": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, j: 2, g: 3}. What is the expected number of occurrences of the pattern 'cj*' in 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 2 by randomly selecting letters from the multiset {s: 1, x: 2, q: 1, n: 2}, what is the expected number of times the pattern 'xs+' 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 {q: 1, c: 1, a: 2, n: 2}. What is the expected number of occurrences of the pattern 'c*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": "When randomly selecting 3 letters from the multiset {x: 1, i: 1, z: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'iz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.92", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {g: 1, f: 1, u: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'g+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {b: 1, f: 4} to form a word, what is the expected number of matches of the pattern 'fb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, a: 2} to form a word, what is the expected number of matches of the pattern 'pa*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 1, f: 1, q: 1, i: 1} 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {c: 1, q: 1, m: 1, n: 1, l: 1}. What is the expected number of occurrences of the pattern 'nl*' in 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 {c: 1, l: 1, r: 2, f: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'j+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 {d: 1, c: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'dc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.92", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, d: 1, o: 1, i: 1}. What is the expected number of occurrences of the pattern 'd+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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {d: 2, u: 3} 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": "1.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {z: 4, d: 2}. What is the expected number of occurrences of the pattern 'z.*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": "0.8", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, a: 2, d: 1}. 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": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {x: 3, p: 2}. 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": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 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 {e: 4, k: 1}, what is the expected number of times the pattern 'k.*e' 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 {e: 2, l: 2, u: 2}. What is the expected number of occurrences of the pattern 'l.*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": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, d: 2}, what is the expected number of times the pattern 'd.*k' 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 2 by randomly selecting letters from the multiset {n: 1, m: 1, e: 2, i: 1, l: 1}, what is the expected number of times the pattern 'li+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.03", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {d: 1, s: 2, x: 1, b: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'ls*'? 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 2 by randomly selecting letters from the multiset {y: 1, v: 2, r: 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": "When randomly selecting 3 letters from the multiset {p: 1, b: 1, g: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'rb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {u: 1, o: 1, k: 1, s: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'u+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 1, c: 1, o: 1, i: 1, q: 1}, what is the expected number of times the pattern 's.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, e: 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": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, l: 1, x: 1, h: 1}. What is the expected number of occurrences of the pattern 'hl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 2, b: 3}, 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": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {l: 1, x: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'x.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, z: 1, q: 1, k: 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": "Form a word by randomly choosing 2 letters from the multiset {y: 1, z: 2, u: 3}. What is the expected number of occurrences of the pattern 'y*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": "1.1", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 2, x: 3}, what is the expected number of times the pattern 'xv+' 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 2 letters from the multiset {j: 2, 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, v: 2}, what is the expected number of times the pattern 'u+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": "When randomly selecting 2 letters from the multiset {e: 1, z: 1, v: 1, y: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'ej+'? 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 2 letters from the multiset {r: 1, j: 1, k: 1, 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": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 1, u: 1, c: 1, t: 1, h: 2}, what is the expected number of times the pattern 'u.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.03", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 2, b: 3, v: 1} to form a word, what is the expected number of matches of the pattern 'v.*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 {v: 2, n: 1, f: 1, o: 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": "0.7", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 2, y: 2, l: 2}, what is the expected number of times the pattern 'y+w' 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 2 letters from the multiset {w: 1, c: 1, x: 1, b: 1, z: 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 {u: 2, d: 1, s: 2, l: 1}, what is the expected number of times the pattern 'd.*s' 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: 1, t: 1, 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": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, b: 2, f: 2}. What is the expected number of occurrences of the pattern 'ee+' in 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 {s: 2, a: 4}. 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 4 letters from the multiset {a: 1, g: 3, e: 4}. What is the expected number of occurrences of the pattern 'e.*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": "1.29", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 5, k: 2}, what is the expected number of times the pattern 'c+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.24", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, k: 1, q: 2, i: 1}, 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": "0.77", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, l: 1, f: 1, h: 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": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 1, j: 1, h: 4, e: 1} to form a word, what is the expected number of matches of the pattern 'j*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, i: 1, d: 2, o: 1}, what is the expected number of times the pattern 'd+e' 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 {j: 1, e: 3, b: 1, z: 1, 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 {s: 1, c: 2, y: 2, m: 1, q: 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": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 1, x: 1, r: 1, f: 3, h: 1} to form a word, what is the expected number of matches of the pattern 'p*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, e: 3, x: 2, r: 2}. What is the expected number of occurrences of the pattern 'x+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": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {h: 1, v: 2, i: 1, r: 1, y: 1} 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": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 1, s: 2, p: 1, z: 1, j: 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": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, u: 3}, what is the expected number of times the pattern 'ud+' 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 {s: 3, p: 4}, 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": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 2, l: 1, x: 2, k: 1, b: 2}. What is the expected number of occurrences of the pattern 'x*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": "0.62", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 3, b: 2, i: 1, y: 2}, what is the expected number of times the pattern 'yc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, q: 2, z: 1, k: 2}. What is the expected number of occurrences of the pattern 'zk*' in 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 4 by randomly selecting letters from the multiset {c: 2, p: 2, z: 1, q: 1}, what is the expected number of times the pattern 'z.*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 4 letters from the multiset {u: 1, i: 2, x: 1, n: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'm*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.77", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, i: 2, p: 4}. What is the expected number of occurrences of the pattern 'iu*' in 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 4 letters from the multiset {g: 2, i: 4}. What is the expected number of occurrences of the pattern 'gi*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.67", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 1, x: 1, e: 3, o: 2}. What is the expected number of occurrences of the pattern 'rx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 1, t: 1, u: 1, w: 2, e: 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": "Form a word by randomly choosing 4 letters from the multiset {c: 2, g: 5, n: 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": "2.14", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, y: 4}, 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": "0.43", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, h: 1, w: 2, g: 1, a: 1}. What is the expected number of occurrences of the pattern 'g+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": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, o: 2, d: 2, 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": "0.9", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, a: 2, q: 3}. What is the expected number of occurrences of the pattern 'qx*' 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 4 letters from the multiset {b: 2, f: 2, e: 1, d: 1}. 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": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, u: 1, n: 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": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, j: 2, r: 2, v: 1}, what is the expected number of times the pattern 'jv*' 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 4 by randomly selecting letters from the multiset {n: 2, s: 2, h: 2, m: 1}, what is the expected number of times the pattern 's+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, u: 2, p: 1, f: 1, c: 3}. 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": "0.32", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 2, s: 3, r: 3}, 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": "2.1", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, k: 1, j: 1, l: 1, h: 1}, what is the expected number of times the pattern 'j.*h' 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 4 letters from the multiset {z: 1, n: 1, m: 1, x: 3}. What is the expected number of occurrences of the pattern 'nx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.42", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 1, k: 1, u: 1, j: 1, n: 2}, 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 {n: 5, y: 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": "0.62", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {n: 1, l: 3, o: 1, z: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 1, a: 5}, what is the expected number of times the pattern 'a.*c' 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 4 by randomly selecting letters from the multiset {h: 3, e: 1, z: 4}, what is the expected number of times the pattern 'ez+' 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 {m: 2, u: 3, s: 1} to form a word, what is the expected number of matches of the pattern 'u+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": "Form a word by randomly choosing 3 letters from the multiset {g: 3, l: 1, d: 2}. 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": "When randomly selecting 3 letters from the multiset {s: 4, z: 1, y: 3} to form a word, what is the expected number of matches of the pattern 'yz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 1, m: 1, j: 1, x: 3, o: 1}, what is the expected number of times the pattern 't.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 2, q: 1, b: 3, r: 1, c: 1} to form a word, what is the expected number of matches of the pattern 's.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 1, h: 3, b: 1, o: 1, j: 2}. 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": "0.55", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 1, g: 2, e: 2, k: 1, f: 2}, 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": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 5, m: 3}, 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": "1.84", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 1, a: 1, y: 2, p: 1, r: 3}, 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": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 2, s: 2, w: 1, o: 1}. What is the expected number of occurrences of the pattern 'ow+' in 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 4 letters from the multiset {e: 3, p: 3}. What is the expected number of occurrences of the pattern 'ep+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, y: 1, z: 2, i: 1, c: 1}, what is the expected number of times the pattern 'z*i' 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: 5, h: 3}, what is the expected number of times the pattern 'h+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.62", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, g: 2, k: 3}, what is the expected number of times the pattern 'k.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, d: 1, t: 3, l: 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 4 letters from the multiset {s: 1, e: 3, k: 2}. 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": "1.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 1, k: 3, m: 2, q: 2}. What is the expected number of occurrences of the pattern 'kk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.36", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 5, r: 3}. What is the expected number of occurrences of the pattern 't+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": "1.27", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, b: 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": "0.45", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, n: 1, v: 2}, what is the expected number of times the pattern 'mv+' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 1, t: 3, a: 2}, what is the expected number of times the pattern 'wa+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 4, z: 3, n: 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": "0.32", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, e: 1, q: 1, t: 1, p: 3} to form a word, what is the expected number of matches of the pattern 'p.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 2, w: 2, i: 1, g: 3} 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": "1.24", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 2, n: 5}. What is the expected number of occurrences of the pattern 'r.*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": "1.43", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, k: 1, a: 2, y: 1, l: 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": "0.57", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 2, x: 2, m: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'i.*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": "When randomly selecting 3 letters from the multiset {s: 2, k: 1, q: 1, o: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'r+s'? 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, b: 6}, 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": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, p: 1, m: 3}, what is the expected number of times the pattern 'p+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 4 letters from the multiset {k: 2, s: 2, t: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'ts*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.47", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, j: 2, g: 2}, 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": "0.43", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, f: 1, z: 1, b: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, o: 2, b: 1}, 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": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, r: 3}. What is the expected number of occurrences of the pattern 'rb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.74", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, o: 1, d: 4}, 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 4 by randomly selecting letters from the multiset {c: 1, f: 2, q: 2, w: 2, h: 1}, what is the expected number of times the pattern 'hq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.62", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 1, w: 3, u: 1, q: 3} to form a word, what is the expected number of matches of the pattern 'lq+'? 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: 4, o: 1, x: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'ya+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, u: 2, j: 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": "0.14", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, b: 2, w: 1, r: 4}, 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": "0.43", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, w: 4}. What is the expected number of occurrences of the pattern 'wb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 2, h: 1, z: 3, e: 1, r: 1}, 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, t: 1, b: 1, s: 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": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 2, z: 2, a: 2, f: 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": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 2, t: 3, m: 1, z: 1}, what is the expected number of times the pattern 'z*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 3, q: 1, c: 3} to form a word, what is the expected number of matches of the pattern 'q*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.93", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, a: 2, f: 1, n: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, i: 3}, what is the expected number of times the pattern 'g.*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": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, a: 1, h: 2, d: 2}, what is the expected number of times the pattern 'd.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.29", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, g: 2, p: 1, b: 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": "0.43", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 1, r: 2, j: 2, d: 1, o: 2}. 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": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, y: 5}, what is the expected number of times the pattern 'y*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.84", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 1, j: 1, f: 1, y: 1, d: 2}, what is the expected number of times the pattern 'd*y' 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 {x: 3, p: 1, h: 1, k: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'y.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, c: 3, i: 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": "0.11", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 5, k: 2, e: 1}. What is the expected number of occurrences of the pattern 'ek+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 1, j: 2, g: 1, f: 1, i: 2}, what is the expected number of times the pattern 'f+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 3, k: 1, x: 1, d: 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": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, p: 3, w: 1, o: 1, x: 1}. What is the expected number of occurrences of the pattern 'n+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": "0.14", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 2, r: 1, g: 1, u: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'nu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 4, y: 2}, 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": "2.67", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {k: 6, m: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'q*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.55", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, g: 1, v: 1, q: 1, k: 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 4 letters from the multiset {m: 2, e: 2, q: 4}. What is the expected number of occurrences of the pattern 'eq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, c: 4, a: 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": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, l: 1, q: 2, b: 1, z: 3} 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": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 3, a: 2, m: 1, e: 1}, what is the expected number of times the pattern 'a.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.29", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 1, j: 2, m: 1, z: 3} to form a word, what is the expected number of matches of the pattern 'j*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {k: 4, v: 2} to form a word, what is the expected number of matches of the pattern 'k+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 2, x: 2, z: 2, g: 2}, what is the expected number of times the pattern 'z+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.24", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 4, n: 3} to form a word, what is the expected number of matches of the pattern 'u+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.29", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, y: 1, l: 3, m: 1, i: 2}. 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": "0.32", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, d: 2, m: 1, y: 2, h: 1}, what is the expected number of times the pattern 'n*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.95", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, m: 1, n: 1, i: 2, p: 2}, what is the expected number of times the pattern 'np*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.62", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, m: 1, j: 4}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {o: 1, f: 3, d: 3, l: 1} 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": "0.16", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {m: 1, n: 2, o: 1, g: 1, h: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 1, q: 2, v: 1, d: 2, 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": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, w: 1, l: 2, b: 2}, 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 4, m: 3, t: 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": "0.64", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 4, l: 3}. What is the expected number of occurrences of the pattern 'l.*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": "1.71", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 4, e: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'w+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, o: 2, y: 1, v: 2, a: 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": "0.53", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 5, q: 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": "1.43", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, j: 1, f: 1, a: 2, v: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 4, n: 3}. What is the expected number of occurrences of the pattern 'u.*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": "1.71", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, x: 1, w: 1, q: 1, l: 1}. What is the expected number of occurrences of the pattern 'x.*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": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 2, x: 5, o: 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": "2.14", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 3, m: 4} to form a word, what is the expected number of matches of the pattern 'n*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 1, b: 1, i: 1, z: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'z*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.77", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, s: 6}, what is the expected number of times the pattern 'u+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.46", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {o: 1, u: 1, c: 1, v: 2, s: 1}. What is the expected number of occurrences of the pattern 'c.*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": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 1, j: 2, n: 1, x: 1, a: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 4, y: 3} to form a word, what is the expected number of matches of the pattern 'y+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.69", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 4, g: 3}, what is the expected number of times the pattern 'x+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.74", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 5, k: 2}. 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": "2.38", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 1, n: 1, c: 1, h: 2, w: 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 {o: 5, p: 2}. 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": "0.67", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 3, c: 3, w: 1} to form a word, what is the expected number of matches of the pattern 'w.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, q: 1, v: 2, e: 3}. What is the expected number of occurrences of the pattern 'yv+' in 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 {a: 2, r: 2, p: 2}, what is the expected number of times the pattern 'p+a' 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 {c: 2, y: 1, f: 5}. What is the expected number of occurrences of the pattern 'fc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.26", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 3, e: 4, x: 1} 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": "0.16", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, y: 2, t: 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": "0.14", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 2, p: 1, e: 3}, 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": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 3, g: 4}. 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": "1.29", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 3, p: 4}, what is the expected number of times the pattern 'p.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.71", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, f: 3, c: 1, j: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, i: 2, a: 1, w: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 4, l: 1, u: 1}, what is the expected number of times the pattern 'ug+' 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": "Form a word by randomly choosing 3 letters from the multiset {b: 2, n: 4, l: 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 {y: 5, e: 3}, what is the expected number of times the pattern 'ey+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, o: 1, z: 3, n: 3}, 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": "0.41", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, e: 3}, what is the expected number of times the pattern 'te+' 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 4 letters from the multiset {s: 2, p: 2, j: 3}. What is the expected number of occurrences of the pattern 's+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": "0.32", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, x: 1, j: 1, p: 1, k: 2}. What is the expected number of occurrences of the pattern 'x+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": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 1, r: 1, v: 1, h: 2, x: 1}. What is the expected number of occurrences of the pattern 'rx+' in 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 4 letters from the multiset {d: 3, x: 3, y: 2}. What is the expected number of occurrences of the pattern 'x+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": "Form a word by randomly choosing 3 letters from the multiset {f: 2, t: 4}. 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 4 letters from the multiset {h: 2, q: 3, k: 1}. What is the expected number of occurrences of the pattern 'k.*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": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, y: 5}, 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": "0.71", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, u: 1, s: 2, l: 2, h: 2}. What is the expected number of occurrences of the pattern 'hl+' in 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 4 by randomly selecting letters from the multiset {e: 3, j: 1, v: 2, c: 2}, what is the expected number of times the pattern 'cv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.24", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, m: 2, v: 1, e: 2, g: 2}. What is the expected number of occurrences of the pattern 'vt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.41", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 2, l: 2, i: 3, a: 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": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, h: 2, a: 1, x: 1}, 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": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 2, l: 3, o: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'z*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.24", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, m: 3}. What is the expected number of occurrences of the pattern 'ml+' in 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 4 letters from the multiset {i: 1, g: 2, t: 2, n: 3}. 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, i: 1, n: 5}, what is the expected number of times the pattern 'n.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.36", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {v: 2, s: 3, h: 2, p: 1} to form a word, what is the expected number of matches of the pattern 's.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, i: 2, z: 1, u: 2, h: 1}, what is the expected number of times the pattern 'm.*h' 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 4 by randomly selecting letters from the multiset {c: 1, j: 2, a: 3, h: 1}, what is the expected number of times the pattern 'h+c' 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 {c: 2, m: 2, i: 2, n: 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 {m: 1, t: 1, u: 1, d: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'u.*m'? 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, x: 1, i: 1, k: 1, n: 4} to form a word, what is the expected number of matches of the pattern 'x*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.41", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 1, w: 2, r: 1, i: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? 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 {q: 1, w: 1, t: 2, m: 2, z: 1}, 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": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 1, d: 2, o: 2, m: 1, z: 2}, 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": "1.24", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, u: 1, e: 3}. What is the expected number of occurrences of the pattern 'e.*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": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, x: 2, i: 1, s: 2}, what is the expected number of times the pattern 's.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.29", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 1, c: 3, w: 2, r: 2} to form a word, what is the expected number of matches of the pattern 'c+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: 3, j: 2, y: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 4, p: 4}, what is the expected number of times the pattern 'pv+' 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 4 by randomly selecting letters from the multiset {f: 5, a: 1, g: 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": "1.19", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 1, u: 2, w: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'wd+'? 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 {f: 1, n: 4, r: 1}. What is the expected number of occurrences of the pattern 'f.*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": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, f: 3, l: 4} to form a word, what is the expected number of matches of the pattern 'l.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {n: 1, v: 3, c: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'n+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 1, w: 2, k: 2, 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": "0.14", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, t: 2, v: 1, b: 1, y: 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": "Form a word by randomly choosing 3 letters from the multiset {z: 2, v: 2, k: 2}. What is the expected number of occurrences of the pattern 'z+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": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 1, m: 3, v: 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": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {q: 3, i: 4, b: 1} to form a word, what is the expected number of matches of the pattern 'ib*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.64", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 1, z: 2, j: 1, e: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'e.*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 4 letters from the multiset {l: 2, j: 1, d: 3, r: 2}. What is the expected number of occurrences of the pattern 'd+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": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, x: 1, t: 1, v: 3}, what is the expected number of times the pattern 'k*v' appears? 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 4 letters from the multiset {x: 5, z: 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": "0.29", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 1, u: 1, i: 1, n: 2, h: 1}, what is the expected number of times the pattern 'hn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, m: 3, p: 3}, what is the expected number of times the pattern 'l*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 4, a: 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": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 2, r: 1, a: 1, m: 1, o: 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 4 letters from the multiset {q: 1, o: 2, x: 2, r: 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": "1.86", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 2, z: 3, d: 3}, what is the expected number of times the pattern 'd+p' 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 {m: 1, s: 3, z: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, h: 3, f: 2}, 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": "0.14", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 4, u: 2} 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": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, a: 3} 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": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 4, y: 2, w: 2} to form a word, what is the expected number of matches of the pattern 'y+w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.24", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 4, t: 1, a: 2}, what is the expected number of times the pattern 'ay*' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 1, q: 1, b: 1, i: 1, g: 2}, what is the expected number of times the pattern 'ib*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.77", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 2, u: 4, l: 2}, 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": "1.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 4, u: 1, d: 1}, 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": "When randomly selecting 3 letters from the multiset {o: 2, h: 2, n: 1, v: 1} 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": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, y: 2, g: 2, s: 1, l: 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": "When randomly selecting 3 letters from the multiset {x: 1, k: 3, d: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 4, b: 3}. What is the expected number of occurrences of the pattern 'm+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": "0.74", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 4, m: 2, q: 2}. What is the expected number of occurrences of the pattern 'm*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": "1.24", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, y: 4}. 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": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 1, q: 3, p: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'q*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 4 by randomly selecting letters from the multiset {g: 6, j: 2}, what is the expected number of times the pattern 'jg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.14", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 2, l: 6}, what is the expected number of times the pattern 'l+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.14", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 3, w: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'w*y'? 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": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 4, d: 3, c: 1}, 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 2, s: 1, d: 4} 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": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, z: 2, v: 1, q: 1}. What is the expected number of occurrences of the pattern 'z+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": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, a: 1, y: 2, o: 3, v: 1}, what is the expected number of times the pattern 'o*a' 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 {q: 3, x: 1, j: 2, w: 1, n: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, k: 1, h: 1, f: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'h+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 4 letters from the multiset {k: 1, a: 2, r: 4} to form a word, what is the expected number of matches of the pattern 'k*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.29", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, b: 2, h: 1, k: 2}, what is the expected number of times the pattern 'k.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 2, f: 2, x: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'ff*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.29", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 2, r: 4}. What is the expected number of occurrences of the pattern 'gr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {k: 1, u: 3, l: 4} to form a word, what is the expected number of matches of the pattern 'u.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, v: 1, a: 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": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 3, a: 4, q: 1}. What is the expected number of occurrences of the pattern 'qa+' in 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 4 letters from the multiset {o: 1, l: 4, g: 1, w: 2}. 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": "0.43", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 1, a: 2, g: 1, e: 1, v: 1}, what is the expected number of times the pattern 'we+' 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 {h: 2, s: 1, d: 1, m: 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": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 4, e: 3}, what is the expected number of times the pattern 'qe*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 3, k: 2, h: 3}, what is the expected number of times the pattern 'h+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": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 2, z: 2, j: 2}, 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": "0.47", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 4, e: 2, h: 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": "0.16", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {o: 3, d: 3} to form a word, what is the expected number of matches of the pattern 'do+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 3, m: 3, 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": "0.64", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, j: 3, b: 3} to form a word, what is the expected number of matches of the pattern 'pp+'? 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 4 by randomly selecting letters from the multiset {y: 3, o: 4}, 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": "1.71", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 1, w: 1, t: 1, v: 1, x: 2}. What is the expected number of occurrences of the pattern 'v.*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": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, s: 2, e: 2, m: 1, g: 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": "0.11", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {v: 3, w: 2, n: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'v*i'? 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 4 letters from the multiset {h: 1, f: 1, n: 1, u: 1, b: 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": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, m: 1, o: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, h: 3, b: 2}. What is the expected number of occurrences of the pattern 'vv*' in 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 {x: 3, c: 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": "When randomly selecting 4 letters from the multiset {j: 2, e: 1, z: 1, u: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'je+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, x: 5} to form a word, what is the expected number of matches of the pattern 'i+x'? 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 {l: 3, t: 2, i: 2} 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": "0.43", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, c: 1, m: 2, f: 1, b: 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": "0.11", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 5, 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": "0.29", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 1, e: 3, k: 1, g: 2} 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": "0.85", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, m: 2, c: 3, l: 1}, what is the expected number of times the pattern 'e+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, h: 1, x: 1, f: 3}, what is the expected number of times the pattern 'x.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.43", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 4, w: 2, p: 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": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, r: 2, k: 1, a: 1, q: 2}. What is the expected number of occurrences of the pattern 'cq+' in 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 {w: 2, s: 1, t: 1, m: 2}, what is the expected number of times the pattern 'st+' 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 {q: 2, d: 4}. 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": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 1, m: 3, y: 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": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, b: 4}, what is the expected number of times the pattern 'c+b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.69", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 3, j: 2, m: 1, h: 2}, what is the expected number of times the pattern 'he+' 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 {b: 3, h: 3}. 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": "0.45", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {y: 4, q: 4}. 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": "1.29", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {v: 1, g: 2, q: 1, z: 1, w: 2} 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": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 2, q: 2, y: 3} to form a word, what is the expected number of matches of the pattern 'q+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, w: 4}. What is the expected number of occurrences of the pattern 'wu*' 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": "When randomly selecting 3 letters from the multiset {s: 1, n: 1, i: 1, e: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'id+'? 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 4 by randomly selecting letters from the multiset {i: 3, c: 2, g: 2}, what is the expected number of times the pattern 'g*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 2, s: 2, u: 2, e: 1}, what is the expected number of times the pattern 'su*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.47", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 1, t: 3, e: 1, p: 1, w: 1}, what is the expected number of times the pattern 'w.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, x: 1, k: 1, e: 2, f: 1}, what is the expected number of times the pattern 'fe+' 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 {a: 2, t: 2, g: 1, k: 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": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 1, b: 3, r: 1, t: 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": "Form a word by randomly choosing 3 letters from the multiset {q: 1, c: 2, d: 3, e: 2}. 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 4 letters from the multiset {a: 2, z: 6}. What is the expected number of occurrences of the pattern 'za*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.71", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 4, c: 1, k: 3}, what is the expected number of times the pattern 'kd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, m: 1, r: 4, w: 1, q: 1}, what is the expected number of times the pattern 'i*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.41", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 4, f: 4}. 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": "0.64", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 6, s: 2}. 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": "0.46", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, p: 1, h: 3, x: 1}, 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": "0.53", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 1, z: 5}, 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 {u: 2, x: 3, s: 3}. What is the expected number of occurrences of the pattern 'x*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": "1.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 4, f: 2}, 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": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 2, z: 6}. What is the expected number of occurrences of the pattern 'z*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": "2.14", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 1, k: 1, j: 1, a: 2, r: 1}, what is the expected number of times the pattern 'k+r' 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 {s: 2, m: 2, r: 1, n: 1, x: 1}, 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": "0.95", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 1, k: 1, y: 2, b: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'cc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.95", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 3, s: 1, e: 1, y: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'e.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 1, l: 1, d: 2, y: 1, w: 1}, what is the expected number of times the pattern 'lw*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.77", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, r: 3, c: 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": "0.31", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 3, k: 3, b: 2}, what is the expected number of times the pattern 'k*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {n: 2, x: 1, b: 5} to form a word, what is the expected number of matches of the pattern 'n+b'? 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 4 by randomly selecting letters from the multiset {d: 1, o: 1, c: 2, n: 1, f: 1}, what is the expected number of times the pattern 'dn+' 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 4 letters from the multiset {w: 2, q: 2, j: 3, c: 1}. What is the expected number of occurrences of the pattern 'cq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.62", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, j: 5}. 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": "2.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 3, e: 1, i: 1, u: 1, g: 1}, what is the expected number of times the pattern 'ou*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.93", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 1, s: 1, z: 2, o: 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": "When randomly selecting 3 letters from the multiset {n: 1, g: 1, f: 1, b: 1, y: 3} to form a word, what is the expected number of matches of the pattern 'g+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 2, o: 3, k: 1} 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": "0.3", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, r: 1, d: 1, p: 3, i: 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": "0.04", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, b: 1, k: 3, f: 3}. What is the expected number of occurrences of the pattern 'gf*' in 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 {o: 1, i: 2, e: 4} 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": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 2, l: 1, y: 1, s: 3}, what is the expected number of times the pattern 'l*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {q: 3, j: 1, w: 1, b: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'm*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.86", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, u: 2}, what is the expected number of times the pattern 'c.*u' 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 4 letters from the multiset {v: 4, l: 2} to form a word, what is the expected number of matches of the pattern 'l+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.93", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 4, r: 3}. What is the expected number of occurrences of the pattern 'ir+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.69", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {s: 3, o: 3, a: 2}, what is the expected number of times the pattern 'os+' 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 {o: 1, h: 1, v: 3, a: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'vo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 1, w: 2, y: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'f*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.53", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, e: 2, y: 1, x: 2, u: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 2, c: 2, k: 3} to form a word, what is the expected number of matches of the pattern 'cj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {m: 2, i: 1, l: 3, t: 1}. What is the expected number of occurrences of the pattern 'm*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": "2.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 1, e: 2, c: 1, n: 2}, 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": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 1, v: 2, n: 1, j: 2, z: 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": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 3, e: 4}, what is the expected number of times the pattern 'e+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.29", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {t: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'tu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, a: 2, n: 2, b: 1}. What is the expected number of occurrences of the pattern 'o*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": "0.53", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, e: 3, k: 2}. What is the expected number of occurrences of the pattern 'u+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": "0.31", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, c: 4, s: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'nc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.68", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, d: 2, a: 1, j: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'd+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": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 4, c: 3}, what is the expected number of times the pattern 's+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.74", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, w: 2, k: 3}, 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 {w: 1, y: 2, l: 3, o: 1, e: 1} 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {b: 1, t: 2, a: 1, d: 1, p: 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": "0.65", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 1, m: 3, g: 2, c: 2}. What is the expected number of occurrences of the pattern 'a.*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": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, t: 3, i: 2}. 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": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {z: 2, v: 4} 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": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 1, r: 1, m: 1, e: 2, y: 2} 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": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, a: 5}, 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": "0.14", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 3, j: 2, u: 3}, what is the expected number of times the pattern 'uy+' 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: 2, e: 4, v: 2}. What is the expected number of occurrences of the pattern 'v.*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": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, i: 1, e: 1, v: 2, f: 2}, what is the expected number of times the pattern 'f.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 1, x: 2, i: 2, a: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 1, n: 2, v: 1, d: 2, y: 1}. What is the expected number of occurrences of the pattern 'v*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": "1.29", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 2, t: 1, q: 2, h: 2, b: 1} to form a word, what is the expected number of matches of the pattern 't.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {u: 5, p: 3}. What is the expected number of occurrences of the pattern 'u*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": "1.84", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 4, d: 4}, 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 2, t: 2, h: 2}, what is the expected number of times the pattern 'te+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.47", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {h: 1, v: 3, q: 1, t: 1, 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": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, f: 2, s: 3} to form a word, what is the expected number of matches of the pattern 'f*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 6, a: 2} to form a word, what is the expected number of matches of the pattern 'ai*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {w: 1, n: 1, u: 2, m: 1, p: 1}. What is the expected number of occurrences of the pattern 'p+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": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 4, s: 3} 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": "1.71", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {f: 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": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 4, z: 3}, 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": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, p: 6}. 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": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 3, l: 2, f: 1, s: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'n+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 2, h: 3, m: 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": "0.64", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {b: 5, q: 1}. What is the expected number of occurrences of the pattern 'q.*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": "1.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 4, u: 4}, what is the expected number of times the pattern 'n+u' 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 4 by randomly selecting letters from the multiset {q: 2, z: 2, h: 4}, what is the expected number of times the pattern 'z*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.24", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 2, p: 2, h: 2}, what is the expected number of times the pattern 'eh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 2, y: 4, m: 2}. What is the expected number of occurrences of the pattern 'k+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": "0.48", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 3, d: 1, u: 1, s: 1}, what is the expected number of times the pattern 'u.*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 4 by randomly selecting letters from the multiset {f: 2, i: 2, p: 1, a: 1, x: 1}, 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": "0.29", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, q: 1, j: 1, l: 2, r: 1}. 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": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 3, h: 1, u: 3} 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": "Form a word by randomly choosing 4 letters from the multiset {t: 2, r: 1, m: 2, y: 1}. What is the expected number of occurrences of the pattern 't+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": "0.23", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 1, q: 2, w: 2, t: 2}, what is the expected number of times the pattern 'w.*t' 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 4 letters from the multiset {p: 4, s: 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": "2.4", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, j: 4}, what is the expected number of times the pattern 'j*h' 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 4 letters from the multiset {i: 2, l: 4, c: 2} 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": "1.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 4, p: 1, y: 2}, 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": "1.71", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 2, k: 6}, what is the expected number of times the pattern 'x+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, u: 1, b: 3} 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": "0.43", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, x: 1, z: 2, p: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'o*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 3, p: 2, h: 1, s: 2}. What is the expected number of occurrences of the pattern 's.*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": "0.32", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {e: 1, r: 1, y: 1, p: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'rp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 2, t: 1, j: 3} to form a word, what is the expected number of matches of the pattern 'jm+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 2, p: 1, d: 2, j: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'hd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.24", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 3, x: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'rx+'? 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 4 letters from the multiset {p: 2, o: 1, f: 2, z: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'fz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.24", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 3, x: 2, k: 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": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, d: 1, c: 5}, what is the expected number of times the pattern 'cd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 1, j: 3, e: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'e*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {t: 1, e: 6}. 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": "4.29", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, v: 1, n: 2, y: 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": "When randomly selecting 4 letters from the multiset {u: 1, o: 3, q: 3, f: 1} to form a word, what is the expected number of matches of the pattern 'qf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 2, n: 1, p: 2, u: 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": "1.29", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 2, i: 1, k: 1, p: 2, o: 1} to form a word, what is the expected number of matches of the pattern 'ip*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {z: 2, e: 3, m: 1, q: 2} to form a word, what is the expected number of matches of the pattern 'mz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.62", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 1, l: 2, d: 2, w: 1}, what is the expected number of times the pattern 'ld*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 1, w: 1, j: 1, q: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'ka+'? 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 {v: 1, j: 2, n: 3, e: 1}. What is the expected number of occurrences of the pattern 'j*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": "1.6", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, g: 4}. What is the expected number of occurrences of the pattern 'dg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 1, m: 2, q: 1, x: 1, k: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 4, i: 2}, what is the expected number of times the pattern 'il*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.67", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, l: 3, x: 1}, 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": "0.13", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 1, y: 1, a: 2, j: 3} to form a word, what is the expected number of matches of the pattern 'j+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.28", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 3, e: 1, j: 1, w: 1, y: 1}, what is the expected number of times the pattern 'yw+' 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 4 by randomly selecting letters from the multiset {i: 4, y: 2}, what is the expected number of times the pattern 'y.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, s: 1, i: 4, t: 2}, what is the expected number of times the pattern 'st*' 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": "Form a word by randomly choosing 3 letters from the multiset {q: 2, c: 3, o: 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": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 3, f: 1, r: 3} to form a word, what is the expected number of matches of the pattern 'f.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.43", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {o: 1, l: 3, v: 2} to form a word, what is the expected number of matches of the pattern 'ov+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.23", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 2, v: 2, j: 1, q: 1, c: 1}, 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": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 1, v: 2, o: 1, t: 3, b: 1} 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": "0.82", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 2, a: 4, m: 2}. What is the expected number of occurrences of the pattern 'au+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 2, k: 3, d: 3}. What is the expected number of occurrences of the pattern 'k*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": "1.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 2, w: 4}. 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": "2.4", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, g: 2, a: 1, d: 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": "When randomly selecting 3 letters from the multiset {i: 1, y: 2, t: 1, f: 1, k: 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": "When randomly selecting 4 letters from the multiset {r: 1, m: 1, x: 1, e: 1, j: 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": "1.29", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, i: 1, c: 2, r: 2, d: 2}. What is the expected number of occurrences of the pattern 'm+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": "When randomly selecting 3 letters from the multiset {s: 1, b: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'sh+'? 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 {z: 1, i: 2, q: 1, g: 2}, what is the expected number of times the pattern 'q.*i' 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 4 letters from the multiset {f: 4, m: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'fn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 3, h: 2, p: 3} 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": "0.32", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {n: 3, h: 4} to form a word, what is the expected number of matches of the pattern 'h*n'? 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 4 by randomly selecting letters from the multiset {t: 3, x: 5}, what is the expected number of times the pattern 't+x' 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 4 letters from the multiset {u: 5, o: 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": "0.64", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 2, f: 1, c: 3} 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": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {h: 4, p: 2, w: 1}. What is the expected number of occurrences of the pattern 'p*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": "2.13", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 2, n: 2, i: 1, t: 1, u: 2}. 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": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 1, f: 1, w: 2, b: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'cf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.64", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, v: 1, m: 2, g: 3}, what is the expected number of times the pattern 'z.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, w: 1, g: 3, e: 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": "0.43", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 2, c: 4}, what is the expected number of times the pattern 'cz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.93", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 3, a: 4}, 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": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 3, z: 3, i: 2}. What is the expected number of occurrences of the pattern 'i+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": "0.23", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 2, b: 1, s: 1, y: 2, z: 1}. What is the expected number of occurrences of the pattern 'i*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": "Form a word by randomly choosing 4 letters from the multiset {k: 2, a: 1, z: 3, j: 1, y: 1}. What is the expected number of occurrences of the pattern 'za*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.66", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, q: 4}, what is the expected number of times the pattern 'q.*t' 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 {j: 3, c: 1, z: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'jq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {e: 5, b: 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": "0.64", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, d: 2, v: 2, m: 2, z: 1}, what is the expected number of times the pattern 'd.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 2, o: 2, m: 2}. What is the expected number of occurrences of the pattern 'g.*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": "When randomly selecting 4 letters from the multiset {v: 2, t: 1, q: 2, s: 1, n: 1} 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": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, m: 3, h: 1}, what is the expected number of times the pattern 'r.*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 {s: 2, n: 5}. What is the expected number of occurrences of the pattern 'sn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.52", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 2, r: 1, g: 1, i: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'r*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.29", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 1, l: 1, x: 1, g: 3} 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": "0.1", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, b: 1, p: 1, h: 2, a: 1}, what is the expected number of times the pattern 'hh*' 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 {h: 1, k: 1, s: 4}. What is the expected number of occurrences of the pattern 's.*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": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 3, o: 1, f: 4}, 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": "When randomly selecting 4 letters from the multiset {v: 3, c: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'v+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.56", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {t: 3, i: 1, n: 1, x: 2} 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": "1.43", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, y: 5}. What is the expected number of occurrences of the pattern 'yo*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.67", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, x: 2, d: 1, l: 4}. 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": "0.64", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 2, n: 2, h: 1, i: 1, k: 1}. 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 4 by randomly selecting letters from the multiset {m: 3, d: 3, q: 1}, 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": "0.28", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 3, d: 1, q: 2}. 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": "0.4", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 3, n: 4}. 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": "1.71", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 2, z: 4} to form a word, what is the expected number of matches of the pattern 'z*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.67", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {b: 3, z: 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": "0.64", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {w: 4, l: 3}. What is the expected number of occurrences of the pattern 'l+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": "1.11", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, u: 1, m: 1, v: 2, j: 2}. What is the expected number of occurrences of the pattern 'i*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": "0.48", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, z: 1, l: 4, t: 1} to form a word, what is the expected number of matches of the pattern 'z+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": "Form a word by randomly choosing 3 letters from the multiset {a: 2, k: 2, w: 1, f: 1, x: 2}. 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": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {f: 3, j: 5}. What is the expected number of occurrences of the pattern 'f.*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": "1.61", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {u: 5, y: 2}. What is the expected number of occurrences of the pattern 'y.*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": "1.43", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {p: 3, x: 1, r: 1, d: 1}. 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 1, f: 1, n: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'xf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.77", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {v: 1, h: 3, s: 2}. What is the expected number of occurrences of the pattern 'h*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": "1.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 3, u: 5} to form a word, what is the expected number of matches of the pattern 'wu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.27", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, w: 2, r: 1, i: 2, d: 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": "0.11", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 1, d: 1, m: 2, p: 2, x: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 4, x: 2, v: 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": "0.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {k: 4, b: 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": "2.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 1, f: 6} to form a word, what is the expected number of matches of the pattern 'h.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 2, h: 1, e: 1, t: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'g*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.53", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, c: 3, j: 3} 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": "0.43", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 1, k: 6, o: 1} to form a word, what is the expected number of matches of the pattern 'ka+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 2, a: 2, l: 2, n: 1, j: 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": "When randomly selecting 3 letters from the multiset {w: 2, h: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'u+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.36", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, n: 2, s: 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": "0.32", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 2, q: 1, a: 1, w: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'qa+'? 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 4 letters from the multiset {i: 2, d: 1, r: 2, e: 1}. What is the expected number of occurrences of the pattern 'i+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": "0.23", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, p: 1, i: 3}. What is the expected number of occurrences of the pattern 'ep*' 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 4 letters from the multiset {q: 1, g: 1, k: 1, o: 2, s: 2}. What is the expected number of occurrences of the pattern 'k.*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": "0.29", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 2, p: 3, i: 3} to form a word, what is the expected number of matches of the pattern 'r*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.36", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 4, m: 4} to form a word, what is the expected number of matches of the pattern 'm+a'? 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: 2, w: 1, b: 1, j: 1}. What is the expected number of occurrences of the pattern 'p*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": "0.53", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 2, o: 3, g: 1, r: 1}, what is the expected number of times the pattern 'ov*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {k: 2, p: 2, j: 1, n: 3} 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": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {k: 3, g: 1, m: 2, i: 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": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, h: 3, f: 1, l: 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": "0.41", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 3, f: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'f*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.07", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, i: 1, m: 2, n: 1, q: 1}, what is the expected number of times the pattern 'm.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.29", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, w: 2, x: 1, v: 1}, 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 2, w: 1, r: 2, c: 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": "0.29", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {r: 4, u: 2, q: 1}. What is the expected number of occurrences of the pattern 'r*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": "1.35", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, r: 1, v: 1, p: 1, x: 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": "0.15", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 2, m: 1, i: 1, c: 4} to form a word, what is the expected number of matches of the pattern 'c+i'? 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 4 letters from the multiset {k: 1, j: 4, f: 2, r: 1} 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": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, f: 4, a: 2, p: 1}, what is the expected number of times the pattern 'a*d' 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 4 letters from the multiset {g: 3, x: 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": "1.2", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {y: 1, t: 1, p: 3, r: 2}. What is the expected number of occurrences of the pattern 'tr*' in 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 {k: 3, z: 4}. What is the expected number of occurrences of the pattern 'kz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.74", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, e: 1, a: 1, y: 3, p: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {o: 1, c: 2, h: 1, n: 1, 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": "When randomly selecting 3 letters from the multiset {o: 3, j: 3} 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": "0.6", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 1, w: 1, y: 1, o: 2, c: 1}, what is the expected number of times the pattern 'u.*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 4 letters from the multiset {d: 3, h: 2, n: 2}. What is the expected number of occurrences of the pattern 'h.*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": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {v: 1, h: 2, f: 3} to form a word, what is the expected number of matches of the pattern 'f*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {s: 2, g: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'v*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {g: 1, r: 4, j: 3} to form a word, what is the expected number of matches of the pattern 'rj*'? 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 4 letters from the multiset {d: 1, n: 1, c: 2, o: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'cc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.11", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, z: 4, v: 1}, what is the expected number of times the pattern 'mz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.66", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {f: 1, w: 1, k: 3, j: 1}. What is the expected number of occurrences of the pattern 'fk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 4, x: 2}, what is the expected number of times the pattern 'x+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.93", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 2, d: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'k+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.47", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 1, m: 1, t: 1, i: 2, g: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, s: 1, o: 2, c: 1, e: 1}, what is the expected number of times the pattern 'e*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.48", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 4, w: 1, e: 1, s: 2}, what is the expected number of times the pattern 'sh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.36", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, v: 1, g: 4}, 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": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {k: 4, w: 2}. What is the expected number of occurrences of the pattern 'wk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.67", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {n: 1, l: 1, z: 2, i: 3} to form a word, what is the expected number of matches of the pattern 'l+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": "When randomly selecting 4 letters from the multiset {r: 3, t: 1, o: 3, q: 1} to form a word, what is the expected number of matches of the pattern 't.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 2, t: 1, c: 1, n: 1, i: 2}, 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 1, a: 1, u: 2, c: 2}. 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": "0.2", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 2, l: 1, x: 2, i: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'i.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.29", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, p: 3}. 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": "2.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {a: 4, j: 3} to form a word, what is the expected number of matches of the pattern 'aj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, n: 1, b: 4}, what is the expected number of times the pattern 'nb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.55", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {f: 1, d: 3, e: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'ed*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.1", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {a: 3, h: 2, e: 1, z: 1}. What is the expected number of occurrences of the pattern 'h*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": "0.73", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 2, z: 1, f: 2, s: 1, j: 2}, what is the expected number of times the pattern 'e*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.62", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {r: 1, o: 1, f: 3, e: 2} to form a word, what is the expected number of matches of the pattern 'e*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 2, b: 2, y: 2}. What is the expected number of occurrences of the pattern 'cy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.47", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, b: 1, z: 3, n: 1}. What is the expected number of occurrences of the pattern 'z*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": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, l: 3, o: 1, z: 1}, what is the expected number of times the pattern 'z.*o' 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 4 letters from the multiset {s: 1, i: 1, z: 2, a: 3, k: 1}. What is the expected number of occurrences of the pattern 'k.*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": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 1, j: 2, h: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'i.*j'? 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 4 letters from the multiset {f: 1, r: 1, j: 1, c: 2, p: 1}. What is the expected number of occurrences of the pattern 'c+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": "0.23", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {q: 4, g: 3}. What is the expected number of occurrences of the pattern 'g*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": "3.4", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {i: 3, b: 3, v: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.86", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 5, k: 1, g: 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": "1.07", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 1, e: 1, a: 1, h: 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": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, l: 1, g: 3, a: 1, d: 2}, what is the expected number of times the pattern 'ha*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.41", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, r: 3, f: 3}, what is the expected number of times the pattern 'sr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {o: 2, e: 1, w: 4}. 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": "1.71", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, p: 2, t: 3, u: 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": "0.32", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, v: 2, q: 2, r: 3}. What is the expected number of occurrences of the pattern 'ri*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.23", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, m: 1, w: 2, s: 2, n: 1}, what is the expected number of times the pattern 'ns+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {p: 2, o: 2, h: 1, y: 2}. What is the expected number of occurrences of the pattern 'ho+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 1, n: 1, s: 1, r: 1, l: 2}, what is the expected number of times the pattern 'l*s' 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 4 letters from the multiset {g: 4, c: 4} to form a word, what is the expected number of matches of the pattern 'cg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.2", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 1, y: 1, i: 2, f: 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": "1.8", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 2, i: 2, v: 2, a: 2}, what is the expected number of times the pattern 'ia*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.24", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {g: 2, t: 4} 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": "2.4", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 7, o: 1} 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": "1.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {i: 1, r: 2, m: 1, o: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'ji*'? 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 {b: 2, z: 5} 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": "1.24", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, s: 3, r: 1, y: 1}, what is the expected number of times the pattern 'kr+' 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 {b: 3, z: 1, t: 3, l: 1}, what is the expected number of times the pattern 'tl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {f: 4, j: 2}. 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": "2.4", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {d: 2, t: 1, h: 2, e: 2, v: 1} 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 {w: 5, i: 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": "2.83", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {w: 1, f: 3, r: 4} to form a word, what is the expected number of matches of the pattern 'f.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.29", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {m: 4, w: 3}. What is the expected number of occurrences of the pattern 'mw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, p: 1, i: 4}, what is the expected number of times the pattern 'i+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.18", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {y: 2, w: 3, o: 2} 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": "0.29", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, o: 1, x: 2}. What is the expected number of occurrences of the pattern 'd*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 {i: 2, v: 5} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 1, c: 4, s: 3} to form a word, what is the expected number of matches of the pattern 'cs*'? 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 4 letters from the multiset {v: 3, x: 5}. What is the expected number of occurrences of the pattern 'x*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": "2.77", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 4, o: 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": "0.43", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 1, w: 2, l: 1, u: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'xu+'? 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 {s: 2, t: 2, 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": "When randomly selecting 3 letters from the multiset {s: 2, q: 4, n: 1} to form a word, what is the expected number of matches of the pattern 'sq+'? 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 4 letters from the multiset {o: 3, p: 1, i: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'o*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.85", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {y: 2, a: 1, q: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'a+y'? 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: 4, d: 2}. What is the expected number of occurrences of the pattern 'fd+' in 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: 2, x: 2, i: 1, l: 1, o: 1}. What is the expected number of occurrences of the pattern 'zx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 4, e: 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": "1.71", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, l: 1, z: 1, t: 2, 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 4, r: 4}, 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": "1.29", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 1, e: 1, v: 1, y: 2, m: 2}, what is the expected number of times the pattern 'qy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 2, n: 2, i: 3, f: 1}, what is the expected number of times the pattern 'ni*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {n: 1, x: 2, i: 1, v: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'x.*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 {o: 3, m: 3} to form a word, what is the expected number of matches of the pattern 'om*'? 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 4 letters from the multiset {j: 4, f: 1, k: 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": "2.4", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, n: 5, c: 2}. What is the expected number of occurrences of the pattern 'n+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": "0.24", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 3 letters from the multiset {k: 2, d: 4} to form a word, what is the expected number of matches of the pattern 'k*d'? 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: 6, v: 2}. What is the expected number of occurrences of the pattern 'lv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.71", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 1, n: 2, e: 2, f: 2}. What is the expected number of occurrences of the pattern 'nf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, w: 2, l: 1, h: 1, e: 1}, what is the expected number of times the pattern 'el*' 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: 1, f: 2, b: 2, k: 1, a: 1}. What is the expected number of occurrences of the pattern 'y+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": "0.05", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 3, n: 1, i: 1, l: 1}, what is the expected number of times the pattern 'lf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.42", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 4, g: 4} 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": "1.29", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 2, a: 1, k: 1, q: 1, b: 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 4 letters from the multiset {j: 1, t: 1, y: 2, b: 2}. 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": "Form a word by randomly choosing 3 letters from the multiset {r: 3, n: 2, o: 1, v: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 2, l: 3, d: 2} to form a word, what is the expected number of matches of the pattern 'p*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.47", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 2, r: 1, k: 2, n: 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": "0.23", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 4, z: 2, s: 1, j: 1}. What is the expected number of occurrences of the pattern 'is+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, q: 3}. What is the expected number of occurrences of the pattern 'dq*' 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"}