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 {m: 1, a: 3}. What is the expected number of occurrences of the pattern 'ma*' in 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 2 letters from the multiset {a: 1, f: 1, j: 2} 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {d: 3, s: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {a: 2, u: 1, t: 1}, what is the expected number of times the pattern 'tu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {m: 1, x: 1, z: 1, d: 1}. 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {s: 2, r: 2}. What is the expected number of occurrences of the pattern 'sr*' 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": "Form a word by randomly choosing 2 letters from the multiset {q: 1, n: 2, x: 1}. 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 2, x: 2}, what is the expected number of times the pattern 'u.*x' 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 {v: 2, w: 2} to form a word, what is the expected number of matches of the pattern 'wv+'? 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 {l: 1, v: 3}, what is the expected number of times the pattern 'v*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {m: 1, l: 1, k: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'k*f'? 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 {q: 1, f: 3}, what is the expected number of times the pattern 'q.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {v: 3, z: 1} to form a word, what is the expected number of matches of the pattern 'vz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 1, w: 1, m: 1, v: 1}, what is the expected number of times the pattern 'vw+' 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 2 letters from the multiset {f: 1, n: 3} to form a word, what is the expected number of matches of the pattern 'nf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {i: 1, u: 2, c: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 2, h: 1, o: 1}, what is the expected number of times the pattern 'h+e' 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 2 by randomly selecting letters from the multiset {h: 1, d: 1, j: 1, l: 1}, what is the expected number of times the pattern 'hl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {r: 2, h: 1, e: 1}. What is the expected number of occurrences of the pattern 'h+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {b: 1, i: 1, p: 1, m: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {t: 1, u: 1, p: 1, i: 1}. What is the expected number of occurrences of the pattern 't.*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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {u: 2, g: 1, e: 1}. What is the expected number of occurrences of the pattern 'eg+' in 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 2 by randomly selecting letters from the multiset {y: 1, w: 1, u: 2}, what is the expected number of times the pattern 'wy+' 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 2 letters from the multiset {r: 1, y: 1, a: 1, h: 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {v: 1, j: 1, f: 1, l: 1}. What is the expected number of occurrences of the pattern 'v*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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {q: 1, w: 3} to form a word, what is the expected number of matches of the pattern 'w*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 1, r: 1, x: 1, h: 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": "When randomly selecting 2 letters from the multiset {q: 1, n: 1, v: 1, 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": "When randomly selecting 2 letters from the multiset {s: 1, u: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'sl+'? 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 {n: 2, j: 2}, what is the expected number of times the pattern 'nj*' appears? 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": "When randomly selecting 2 letters from the multiset {h: 1, c: 1, k: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'kc*'? 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 {d: 1, i: 1, w: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'i*w'? 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 {k: 2, a: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'a+k'? 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 {a: 1, u: 1, w: 1, i: 1}, what is the expected number of times the pattern 'iw+' 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 2 letters from the multiset {f: 3, a: 1}. What is the expected number of occurrences of the pattern 'af+' in 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": "If you form a word of length 2 by randomly selecting letters from the multiset {k: 1, h: 2, y: 1}, what is the expected number of times the pattern 'hy+' 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 {j: 3, k: 1} to form a word, what is the expected number of matches of the pattern 'kj+'? 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 {m: 1, v: 1, t: 2}, what is the expected number of times the pattern 'vm*' 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": "Form a word by randomly choosing 2 letters from the multiset {p: 2, j: 1, i: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {d: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'm+d'? 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 {y: 3, u: 1}. 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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {m: 3, k: 1}. What is the expected number of occurrences of the pattern 'km+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {f: 2, p: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'n*f'? 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 2 letters from the multiset {j: 1, o: 2, i: 1}. What is the expected number of occurrences of the pattern 'jo+' in 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 {l: 2, k: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {r: 1, x: 2, k: 1}. What is the expected number of occurrences of the pattern 'k*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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {o: 2, e: 2}. What is the expected number of occurrences of the pattern 'eo+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 1, d: 1, o: 2}, what is the expected number of times the pattern 'do*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {e: 2, x: 1, h: 1}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {e: 1, j: 1, q: 1, f: 1}. What is the expected number of occurrences of the pattern 'jf*' in 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": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 1, t: 1, j: 1, u: 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": "Form a word by randomly choosing 2 letters from the multiset {k: 1, z: 1, s: 1, a: 1}. What is the expected number of occurrences of the pattern 'az*' in 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 2 letters from the multiset {f: 1, j: 3} 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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 2, s: 2}, what is the expected number of times the pattern 'sy+' 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 {n: 1, i: 2, a: 1}, what is the expected number of times the pattern 'in+' 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 2 by randomly selecting letters from the multiset {t: 1, d: 1, u: 1, w: 1}, what is the expected number of times the pattern 'w.*d' 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 2 letters from the multiset {t: 1, m: 1, b: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'ss*'? 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 {q: 1, m: 2, s: 1}. What is the expected number of occurrences of the pattern 'q*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {m: 2, u: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {u: 2, k: 2}. What is the expected number of occurrences of the pattern 'ku+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {s: 1, h: 1, r: 1, a: 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 {d: 1, l: 1, b: 2}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 2, n: 2}, what is the expected number of times the pattern 'wn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 1, c: 1, p: 1, b: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {d: 3, s: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {v: 2, k: 2}. What is the expected number of occurrences of the pattern 'k*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 1, h: 2, i: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {p: 1, b: 1, z: 1, k: 1}. What is the expected number of occurrences of the pattern 'p+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {j: 1, b: 2, l: 1}, what is the expected number of times the pattern 'lb+' 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 2 letters from the multiset {m: 2, b: 1, a: 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 {q: 1, f: 1, d: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 1, f: 2, a: 1}, what is the expected number of times the pattern 'f+a' 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 {o: 2, f: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {x: 1, w: 1, c: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'qw*'? 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": "Form a word by randomly choosing 2 letters from the multiset {y: 2, a: 1, r: 1}. What is the expected number of occurrences of the pattern 'ya+' in 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 2 letters from the multiset {v: 2, j: 1, r: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {j: 1, h: 1, s: 1, w: 1}, 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 1, i: 1, y: 1, t: 1}, what is the expected number of times the pattern 'in*' 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 {n: 1, a: 1, u: 1, 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 2 letters from the multiset {z: 1, v: 1, m: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'z+w'? 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 2 letters from the multiset {p: 1, z: 2, b: 1}. What is the expected number of occurrences of the pattern 'pz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {p: 2, n: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'fp*'? 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 {v: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {b: 1, j: 2, c: 1} 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 1, z: 1, b: 1, h: 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": "When randomly selecting 2 letters from the multiset {v: 1, t: 1, n: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {a: 1, y: 1, e: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {n: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'm+n'? 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 {n: 1, l: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {r: 1, v: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'v+s'? 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 {o: 1, u: 1, f: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'df*'? 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 {k: 1, g: 3}, what is the expected number of times the pattern 'g*k' 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 {f: 3, g: 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": "When randomly selecting 2 letters from the multiset {d: 1, a: 3} to form a word, what is the expected number of matches of the pattern 'a.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {b: 2, x: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {z: 1, d: 1, w: 1, t: 1}. 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {j: 1, f: 2, t: 1}. What is the expected number of occurrences of the pattern 'j+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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 2, a: 1, z: 1}, what is the expected number of times the pattern 'z+a' 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 2 letters from the multiset {u: 1, s: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'e*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {l: 2, e: 1, n: 1}. What is the expected number of occurrences of the pattern 'n.*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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {h: 1, k: 1, e: 1, s: 1}. 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {m: 1, e: 1, j: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {k: 2, n: 1, q: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 2, w: 1, n: 1}, what is the expected number of times the pattern 'wq+' 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 2 by randomly selecting letters from the multiset {k: 3, w: 1}, what is the expected number of times the pattern 'w+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 1, g: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 1, q: 1, i: 1, n: 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {x: 2, t: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {s: 1, d: 1, e: 1, n: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {u: 1, z: 2, l: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {m: 3, e: 1}. What is the expected number of occurrences of the pattern 'm.*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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {k: 1, z: 3} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 3, n: 1}, what is the expected number of times the pattern 'nh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 1, f: 1, v: 1, k: 1}, what is the expected number of times the pattern 'fd*' 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": "When randomly selecting 2 letters from the multiset {h: 1, c: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'c*a'? 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: 2, l: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'k.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 1, v: 3}, what is the expected number of times the pattern 'v.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {o: 1, k: 3} 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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {z: 1, l: 1, b: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {x: 1, u: 1, g: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 1, c: 2, j: 1}, what is the expected number of times the pattern 'cj+' 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 2 by randomly selecting letters from the multiset {v: 2, x: 1, j: 1}, what is the expected number of times the pattern 'vj*' 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 2 letters from the multiset {b: 1, w: 1, r: 2}. 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 2 letters from the multiset {d: 1, n: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {v: 1, e: 1, f: 2} to form a word, what is the expected number of matches of the pattern 'ev*'? 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 {r: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'r*u'? 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 2 letters from the multiset {k: 1, e: 3}. What is the expected number of occurrences of the pattern 'ke+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {u: 3, p: 1} to form a word, what is the expected number of matches of the pattern 'u*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {i: 2, 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {x: 1, v: 2, w: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {j: 1, z: 1, r: 1, o: 1}. What is the expected number of occurrences of the pattern 'ro*' in 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": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 1, b: 1, v: 1, r: 1}, what is the expected number of times the pattern 'nr*' 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": "Form a word by randomly choosing 2 letters from the multiset {q: 1, n: 2, a: 1}. What is the expected number of occurrences of the pattern 'na*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {c: 2, j: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {x: 1, i: 1, p: 1, c: 1}. What is the expected number of occurrences of the pattern 'pc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {w: 1, j: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'w.*j'? 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 {y: 1, c: 3}. What is the expected number of occurrences of the pattern 'c*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {q: 1, n: 2, c: 1}. What is the expected number of occurrences of the pattern 'nc*' 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 2 by randomly selecting letters from the multiset {y: 1, n: 1, p: 1, g: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 2, z: 1, c: 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 2 by randomly selecting letters from the multiset {m: 2, c: 1, n: 1}, what is the expected number of times the pattern 'nc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {n: 1, d: 1, g: 1, j: 1}. What is the expected number of occurrences of the pattern 'j.*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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {q: 3, y: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {i: 1, r: 1, x: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 1, q: 2, x: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {a: 2, b: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'ab*'? 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 {u: 1, f: 2, n: 1} 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {l: 1, b: 1, d: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'ub+'? 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 2 letters from the multiset {v: 1, j: 2, z: 1}. What is the expected number of occurrences of the pattern 'v*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {x: 1, v: 1, l: 2} 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": "1.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 2, h: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {q: 1, y: 1, p: 2} to form a word, what is the expected number of matches of the pattern 'py+'? 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 {e: 1, i: 1, l: 1, k: 1}. What is the expected number of occurrences of the pattern 'ik+' in 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 2 by randomly selecting letters from the multiset {v: 1, r: 1, q: 1, m: 1}, what is the expected number of times the pattern 'm+v' 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 2 letters from the multiset {f: 2, u: 2}. What is the expected number of occurrences of the pattern 'u*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {f: 1, e: 1, w: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'e.*b'? 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 2 letters from the multiset {l: 2, p: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 1, y: 1, g: 1, f: 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": "When randomly selecting 2 letters from the multiset {k: 1, l: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'lf*'? 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 {l: 1, r: 1, s: 1, b: 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 2, f: 1, e: 1}, what is the expected number of times the pattern 'e.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {a: 1, p: 1, w: 1, r: 1}, 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {n: 1, d: 1, q: 1, s: 1}. What is the expected number of occurrences of the pattern 'd+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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {a: 2, y: 1, s: 1}. 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 1, m: 1, i: 1, q: 1}, what is the expected number of times the pattern 'qi*' 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": "When randomly selecting 2 letters from the multiset {o: 1, a: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {s: 2, v: 1, o: 1}. What is the expected number of occurrences of the pattern 'o+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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {c: 3, o: 1} to form a word, what is the expected number of matches of the pattern 'c*o'? 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 2 letters from the multiset {l: 1, m: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'm*l'? 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 {p: 1, o: 3} to form a word, what is the expected number of matches of the pattern 'p.*o'? 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 {a: 1, p: 1, i: 2}, what is the expected number of times the pattern 'a.*p' 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 {d: 2, a: 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": "Form a word by randomly choosing 2 letters from the multiset {y: 1, x: 1, z: 1, k: 1}. 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {k: 1, e: 1, p: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {q: 2, g: 2}. What is the expected number of occurrences of the pattern 'gq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {i: 1, l: 1, b: 1, u: 1}, what is the expected number of times the pattern 'i+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {w: 2, g: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'gz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 1, p: 1, m: 2}, what is the expected number of times the pattern 'pm*' appears? 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 {r: 2, n: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 1, d: 1, r: 2}, what is the expected number of times the pattern 'n.*d' 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: 1, f: 1, w: 2}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {e: 1, m: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {r: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {i: 2, n: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {a: 1, p: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'p+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 2, h: 2}, what is the expected number of times the pattern 'hp*' appears? 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 2 by randomly selecting letters from the multiset {f: 1, w: 1, g: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {l: 2, k: 2}, what is the expected number of times the pattern 'l.*k' 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 {w: 2, n: 2}, what is the expected number of times the pattern 'w*n' appears? 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 2 by randomly selecting letters from the multiset {r: 1, i: 3}, what is the expected number of times the pattern 'i+r' 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 {k: 1, l: 1, b: 2}, what is the expected number of times the pattern 'l*k' 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": "Form a word by randomly choosing 2 letters from the multiset {t: 1, l: 2, y: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {o: 1, e: 1, h: 1, q: 1}. What is the expected number of occurrences of the pattern 'h+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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {z: 1, i: 1, n: 2}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {v: 1, c: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {s: 1, t: 1, j: 1, u: 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {y: 1, c: 1, k: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'yk*'? 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": "Form a word by randomly choosing 2 letters from the multiset {v: 1, u: 1, c: 1, p: 1}. What is the expected number of occurrences of the pattern 'c*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {a: 3, k: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {f: 1, v: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'v.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {y: 1, f: 3} to form a word, what is the expected number of matches of the pattern 'yf+'? 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 {n: 2, m: 2}, what is the expected number of times the pattern 'n+m' 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 {i: 1, f: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'c.*f'? 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 {t: 1, w: 1, g: 1, u: 1} 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {f: 1, s: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'fr+'? 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 2 letters from the multiset {r: 1, c: 3}. What is the expected number of occurrences of the pattern 'r*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": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {i: 1, p: 1, z: 1, l: 1}. What is the expected number of occurrences of the pattern 'z*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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 2, a: 2}, what is the expected number of times the pattern 'm.*a' 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 {w: 1, m: 1, v: 1, k: 1}, what is the expected number of times the pattern 'm.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {a: 2, f: 1, q: 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {d: 1, x: 1, g: 1, p: 1}. What is the expected number of occurrences of the pattern 'd*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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {y: 2, a: 1, f: 1}. What is the expected number of occurrences of the pattern 'y.*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 2 letters from the multiset {u: 2, i: 2}. What is the expected number of occurrences of the pattern 'u+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {a: 1, j: 1, m: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'a.*m'? 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 {d: 2, u: 1, f: 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": "1.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {s: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'k.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 2, e: 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": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 1, n: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 1, l: 1, x: 2}, what is the expected number of times the pattern 'xo+' 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 2 letters from the multiset {w: 3, u: 1}. What is the expected number of occurrences of the pattern 'u*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 1, e: 1, n: 1, p: 1}, what is the expected number of times the pattern 'en*' 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": "Form a word by randomly choosing 2 letters from the multiset {y: 1, v: 1, a: 1, w: 1}. What is the expected number of occurrences of the pattern 'v.*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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {x: 2, e: 2}. What is the expected number of occurrences of the pattern 'xe*' 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 2 by randomly selecting letters from the multiset {f: 2, a: 1, x: 1}, what is the expected number of times the pattern 'fa*' 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 2 letters from the multiset {r: 2, d: 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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {s: 1, d: 3}. 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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {t: 1, r: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'r.*n'? 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, q: 1, l: 1, p: 1}, what is the expected number of times the pattern 'n.*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 2 by randomly selecting letters from the multiset {w: 1, h: 1, k: 1, y: 1}, what is the expected number of times the pattern 'k.*y' 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 2 letters from the multiset {r: 1, k: 1, x: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {u: 3, g: 1} to form a word, what is the expected number of matches of the pattern 'ug+'? 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 {a: 1, h: 1, f: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 2, e: 2}, 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": "1.33", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {f: 1, a: 1, j: 1, g: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {o: 1, f: 1, u: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'd+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {k: 1, l: 3} to form a word, what is the expected number of matches of the pattern 'kl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {o: 1, j: 3} to form a word, what is the expected number of matches of the pattern 'j*o'? 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 {h: 1, l: 1, t: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {l: 1, r: 1, m: 1, s: 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": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 1, q: 1, y: 1, s: 1}, what is the expected number of times the pattern 'p.*s' 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 {c: 1, u: 1, i: 1, o: 1}, 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {m: 2, q: 2} to form a word, what is the expected number of matches of the pattern 'qm+'? 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 {n: 2, l: 2}, what is the expected number of times the pattern 'nl+' 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 {a: 1, f: 1, k: 2}, what is the expected number of times the pattern 'f.*a' 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 {v: 2, x: 2}, what is the expected number of times the pattern 'x*v' appears? 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 2 by randomly selecting letters from the multiset {p: 2, v: 2}, what is the expected number of times the pattern 'p.*v' 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": "Form a word by randomly choosing 2 letters from the multiset {a: 2, o: 2}. What is the expected number of occurrences of the pattern 'ao*' 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 2 by randomly selecting letters from the multiset {f: 1, l: 1, u: 1, e: 1}, what is the expected number of times the pattern 'u+e' 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 {t: 1, s: 1, p: 1, u: 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {o: 1, z: 1, r: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'm.*z'? 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 {j: 3, x: 1} to form a word, what is the expected number of matches of the pattern 'x.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {a: 2, w: 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": "1.33", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {a: 1, f: 1, p: 1, m: 1}. What is the expected number of occurrences of the pattern 'f*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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {a: 2, e: 1, n: 1}. What is the expected number of occurrences of the pattern 'ne+' in 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 {g: 1, s: 1, c: 1, n: 1}. What is the expected number of occurrences of the pattern 'g+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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {j: 1, i: 2, g: 1}. What is the expected number of occurrences of the pattern 'j+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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {l: 1, v: 1, e: 1, k: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 1, q: 1, d: 2}, what is the expected number of times the pattern 'v+d' 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 {o: 3, c: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {i: 1, t: 3} 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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {h: 1, y: 2, m: 1}. What is the expected number of occurrences of the pattern 'hy*' in 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 2 letters from the multiset {f: 2, i: 1, n: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {l: 2, z: 1, a: 1} 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {z: 2, g: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 1, a: 1, b: 2}, what is the expected number of times the pattern 'am*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 1, q: 2, h: 1}, what is the expected number of times the pattern 'qx*' 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": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 1, x: 1, s: 2}, what is the expected number of times the pattern 'sp*' 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": "If you form a word of length 2 by randomly selecting letters from the multiset {b: 2, v: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {r: 1, h: 1, g: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'g+r'? 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 {a: 1, f: 1, m: 1, q: 1}, what is the expected number of times the pattern 'f+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": "Form a word by randomly choosing 2 letters from the multiset {h: 1, x: 2, l: 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 2 letters from the multiset {m: 1, p: 1, f: 1, s: 1}. What is the expected number of occurrences of the pattern 'mp*' in 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": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 1, v: 1, i: 1, t: 1}, what is the expected number of times the pattern 't.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {d: 2, n: 2}. What is the expected number of occurrences of the pattern 'dn*' 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": "Form a word by randomly choosing 2 letters from the multiset {z: 2, y: 1, v: 1}. What is the expected number of occurrences of the pattern 'y*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": "1.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {i: 3, s: 1}. What is the expected number of occurrences of the pattern 'si+' in 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": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 1, k: 1, a: 1, d: 1}, 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {m: 1, w: 1, l: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'm+w'? 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 {w: 1, d: 1, u: 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {x: 1, i: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {r: 2, n: 2} 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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {j: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'jy*'? 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 2 by randomly selecting letters from the multiset {l: 2, s: 1, b: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {f: 1, b: 2, s: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {m: 1, j: 1, z: 1, f: 1}. What is the expected number of occurrences of the pattern 'm*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {p: 1, i: 1, n: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'c*n'? 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 {o: 1, e: 1, u: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 1, z: 1, n: 2}, what is the expected number of times the pattern 'n.*c' 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 2 letters from the multiset {b: 1, i: 1, k: 1, w: 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 2 by randomly selecting letters from the multiset {d: 2, f: 1, c: 1}, what is the expected number of times the pattern 'd+c' 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 2 by randomly selecting letters from the multiset {x: 1, t: 1, z: 1, c: 1}, 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {e: 1, g: 3}. What is the expected number of occurrences of the pattern 'eg*' in 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 {o: 1, h: 1, a: 1, m: 1}. What is the expected number of occurrences of the pattern 'oh+' in 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": "When randomly selecting 2 letters from the multiset {m: 2, z: 1, o: 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 2 by randomly selecting letters from the multiset {r: 3, s: 1}, 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": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 1, i: 1, k: 1, u: 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": "Form a word by randomly choosing 2 letters from the multiset {j: 1, m: 3}. What is the expected number of occurrences of the pattern 'm+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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {j: 1, a: 1, m: 1, s: 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": "When randomly selecting 2 letters from the multiset {j: 1, k: 1, z: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'j.*s'? 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 {p: 1, c: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'p+c'? 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 2 letters from the multiset {u: 3, t: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {m: 2, q: 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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {d: 1, i: 1, f: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'y+i'? 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 {o: 1, l: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'ol*'? 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 {d: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'd*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {d: 2, o: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'ot*'? 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 {h: 2, l: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'lp*'? 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 {c: 2, m: 1, t: 1}, what is the expected number of times the pattern 'ct+' 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 2 letters from the multiset {y: 1, h: 1, d: 1, b: 1}. What is the expected number of occurrences of the pattern 'dh*' in 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": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 2, i: 2}, 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {m: 2, x: 2}. What is the expected number of occurrences of the pattern 'm*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": "1.33", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {a: 1, h: 2, m: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {z: 1, t: 1, w: 1, o: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 1, y: 1, d: 1, o: 1}, what is the expected number of times the pattern 'd*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 3, b: 1}, what is the expected number of times the pattern 'dd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {r: 1, g: 3} to form a word, what is the expected number of matches of the pattern 'rg*'? 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 {n: 1, i: 1, z: 1, j: 1}, what is the expected number of times the pattern 'i.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 2, r: 1, q: 1}, what is the expected number of times the pattern 'r+q' 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 {c: 1, b: 1, p: 1, m: 1}, what is the expected number of times the pattern 'pp*' 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 {i: 3, m: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {q: 2, j: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 2, e: 1, r: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 2, z: 1, w: 1}, what is the expected number of times the pattern 'gz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {x: 1, z: 3} to form a word, what is the expected number of matches of the pattern 'xz*'? 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 {m: 1, x: 2, r: 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 {p: 1, k: 1, i: 1, b: 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, l: 1, u: 1, c: 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 {s: 1, e: 1, u: 2}, 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": "0.67", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {e: 1, w: 3} to form a word, what is the expected number of matches of the pattern 'we+'? 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 {i: 1, h: 1, t: 2}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {d: 3, g: 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 2 letters from the multiset {h: 2, i: 2}. What is the expected number of occurrences of the pattern 'ih+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 3, x: 1}, what is the expected number of times the pattern 'x+q' 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 {p: 1, v: 3}, 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 2 by randomly selecting letters from the multiset {u: 2, z: 2}, 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": "1.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {m: 1, v: 1, b: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'm.*b'? 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 2 letters from the multiset {i: 1, j: 1, h: 1, z: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 1, i: 1, u: 1, x: 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 2 letters from the multiset {q: 1, o: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'ql*'? 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 {p: 2, u: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'u+p'? 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 {m: 1, e: 1, d: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'dq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {x: 1, z: 1, b: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'x*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {c: 2, e: 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": "When randomly selecting 2 letters from the multiset {e: 1, y: 2, l: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 1, l: 1, q: 2}, what is the expected number of times the pattern 'pl*' 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": "Form a word by randomly choosing 2 letters from the multiset {h: 1, k: 1, u: 1, v: 1}. 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {h: 2, r: 2}. What is the expected number of occurrences of the pattern 'hr+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 3, 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": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 2, t: 1, x: 1}, 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 1, k: 1, j: 1, x: 1}, what is the expected number of times the pattern 'jx*' 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 {b: 1, n: 2, 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 2 by randomly selecting letters from the multiset {m: 1, e: 1, c: 1, v: 1}, what is the expected number of times the pattern 'ec*' 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": "Form a word by randomly choosing 2 letters from the multiset {v: 1, l: 1, e: 1, t: 1}. What is the expected number of occurrences of the pattern 'v+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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {z: 1, r: 1, i: 1, a: 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": "When randomly selecting 2 letters from the multiset {w: 1, d: 1, o: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {l: 2, e: 2}. What is the expected number of occurrences of the pattern 'le+' in 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 {a: 1, x: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'a*e'? 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 2 letters from the multiset {x: 1, d: 1, w: 1, v: 1}. What is the expected number of occurrences of the pattern 'w*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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {n: 1, v: 1, q: 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 1, t: 1, m: 1, f: 1}, what is the expected number of times the pattern 'pt*' 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 {b: 2, t: 1, v: 1}, what is the expected number of times the pattern 'v*b' 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": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 1, l: 1, v: 1, g: 1}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 2, h: 2}, what is the expected number of times the pattern 'hc+' 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": "Form a word by randomly choosing 2 letters from the multiset {a: 2, p: 2}. What is the expected number of occurrences of the pattern 'pa+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {q: 2, j: 2} 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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 3, l: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {t: 1, s: 1, j: 1, e: 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {j: 1, o: 1, n: 1, a: 1}. What is the expected number of occurrences of the pattern 'j.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {g: 2, f: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {f: 1, l: 1, y: 2}. What is the expected number of occurrences of the pattern 'l*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": "1.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {m: 3, u: 1} to form a word, what is the expected number of matches of the pattern 'mu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {i: 1, e: 1, n: 1, p: 1}. What is the expected number of occurrences of the pattern 'i.*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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {y: 1, q: 1, j: 1, v: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 2, v: 2}, what is the expected number of times the pattern 'v*c' appears? 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 2 by randomly selecting letters from the multiset {n: 1, a: 2, c: 1}, what is the expected number of times the pattern 'c.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {e: 1, z: 1, p: 2}. What is the expected number of occurrences of the pattern 'z.*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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {o: 1, b: 1, z: 1, j: 1}. What is the expected number of occurrences of the pattern 'j.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {m: 1, f: 1, u: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'vm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {f: 1, h: 1, j: 1, r: 1}. What is the expected number of occurrences of the pattern 'hf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {z: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 2, n: 2}, what is the expected number of times the pattern 'n.*g' 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 {h: 1, g: 1, s: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'h.*g'? 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 2 letters from the multiset {b: 2, n: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {t: 1, a: 2, d: 1}. What is the expected number of occurrences of the pattern 't.*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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 1, v: 2, q: 1}, what is the expected number of times the pattern 'vn+' 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 2 by randomly selecting letters from the multiset {m: 1, c: 3}, what is the expected number of times the pattern 'cm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 1, y: 1, m: 1, z: 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": "When randomly selecting 2 letters from the multiset {v: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {h: 1, j: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'j*h'? 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": "If you form a word of length 2 by randomly selecting letters from the multiset {b: 1, p: 1, h: 1, x: 1}, what is the expected number of times the pattern 'pp+' 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 {z: 1, b: 1, o: 2}, what is the expected number of times the pattern 'oz+' 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 2 letters from the multiset {a: 1, w: 3}. What is the expected number of occurrences of the pattern 'aw*' in 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 2 by randomly selecting letters from the multiset {b: 1, o: 2, u: 1}, what is the expected number of times the pattern 'ub+' 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 2 letters from the multiset {q: 1, v: 1, g: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'qv*'? 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 {s: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'p*s'? 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 2 by randomly selecting letters from the multiset {s: 1, h: 1, b: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {x: 2, t: 2}. What is the expected number of occurrences of the pattern 'xt*' 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 2 by randomly selecting letters from the multiset {d: 2, c: 1, k: 1}, 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {u: 1, i: 1, v: 1, e: 1}. 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {z: 3, d: 1}. 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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {e: 1, c: 1, f: 1, p: 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": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 2, t: 1, i: 1}, what is the expected number of times the pattern 'tf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {d: 1, x: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'd.*z'? 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 2 letters from the multiset {y: 1, z: 1, d: 1, p: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {m: 1, w: 2, z: 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 2 letters from the multiset {f: 1, x: 2, w: 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": "Form a word by randomly choosing 2 letters from the multiset {a: 2, g: 1, w: 1}. 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {t: 1, r: 1, j: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {n: 1, m: 1, k: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {f: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {i: 1, n: 3}. What is the expected number of occurrences of the pattern 'in+' in 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 2 letters from the multiset {k: 3, o: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {q: 1, j: 1, w: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'n*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {d: 1, y: 2, b: 1}. What is the expected number of occurrences of the pattern 'dy*' in 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 2 letters from the multiset {c: 2, x: 2}. What is the expected number of occurrences of the pattern 'xc*' 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": "Form a word by randomly choosing 2 letters from the multiset {v: 3, g: 1}. What is the expected number of occurrences of the pattern 'gv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {p: 2, f: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'w.*f'? 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 2 letters from the multiset {d: 1, c: 1, t: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {y: 1, z: 1, s: 1, c: 1}. 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {a: 2, h: 2}. What is the expected number of occurrences of the pattern 'a+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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 1, x: 1, k: 2}, what is the expected number of times the pattern 'e*x' 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": "Form a word by randomly choosing 2 letters from the multiset {a: 1, z: 1, y: 1, v: 1}. What is the expected number of occurrences of the pattern 'vy+' in 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 {t: 2, v: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {k: 1, m: 1, e: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'em*'? 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 {d: 1, u: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'd.*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": "Form a word by randomly choosing 2 letters from the multiset {k: 2, s: 1, p: 1}. What is the expected number of occurrences of the pattern 'ps*' in 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": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 1, z: 2, a: 1}, what is the expected number of times the pattern 'a.*z' 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 2 by randomly selecting letters from the multiset {r: 1, g: 1, h: 1, c: 1}, what is the expected number of times the pattern 'hr*' 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: 2, g: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {g: 1, v: 3}. What is the expected number of occurrences of the pattern 'g+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": "If you form a word of length 2 by randomly selecting letters from the multiset {a: 3, r: 1}, what is the expected number of times the pattern 'a+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {s: 1, z: 3} to form a word, what is the expected number of matches of the pattern 's.*z'? 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 {e: 1, q: 1, l: 2}. What is the expected number of occurrences of the pattern 'l*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": "0.67", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {o: 1, m: 1, b: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'mo*'? 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 {q: 1, e: 1, d: 1, j: 1}, what is the expected number of times the pattern 'd+q' 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 2 letters from the multiset {b: 1, s: 1, a: 1, l: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 1, y: 3}, 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": "Form a word by randomly choosing 2 letters from the multiset {j: 1, g: 1, e: 1, o: 1}. What is the expected number of occurrences of the pattern 'o*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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {c: 1, n: 1, j: 1, l: 1}. What is the expected number of occurrences of the pattern 'jc*' in 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": "If you form a word of length 2 by randomly selecting letters from the multiset {z: 1, j: 1, p: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {j: 2, a: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'ja+'? 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 {t: 2, j: 2} to form a word, what is the expected number of matches of the pattern 'j*t'? 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": "When randomly selecting 2 letters from the multiset {h: 1, j: 1, s: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 1, g: 1, e: 1, t: 1}, what is the expected number of times the pattern 't+e' 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 {z: 3, g: 1}, 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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 3, y: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {b: 1, r: 1, f: 1, u: 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": "When randomly selecting 2 letters from the multiset {e: 1, j: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'ea+'? 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 {m: 1, t: 3}, 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": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {u: 1, s: 3}. What is the expected number of occurrences of the pattern 'su+' in 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": "If you form a word of length 2 by randomly selecting letters from the multiset {i: 1, l: 1, d: 2}, what is the expected number of times the pattern 'i*l' 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 {a: 1, o: 1, m: 2}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {t: 1, z: 1, q: 1, j: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {h: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'h.*m'? 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 {e: 1, j: 1, q: 1, r: 1}, what is the expected number of times the pattern 'q+e' 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 {r: 3, g: 1}, what is the expected number of times the pattern 'r*g' 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 {i: 1, y: 1, s: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {r: 2, f: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 1, f: 1, e: 1, s: 1}, what is the expected number of times the pattern 'e.*f' 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 2 letters from the multiset {c: 1, a: 1, j: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'c.*a'? 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 {t: 1, e: 3} to form a word, what is the expected number of matches of the pattern 'et+'? 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 {j: 1, i: 3}, what is the expected number of times the pattern 'ji+' 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 {t: 1, f: 1, n: 2}. What is the expected number of occurrences of the pattern 'fn*' in 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": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 1, e: 1, k: 1, j: 1}, what is the expected number of times the pattern 'ek*' 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": "Form a word by randomly choosing 2 letters from the multiset {h: 2, n: 1, v: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {h: 1, g: 2, e: 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 2 letters from the multiset {y: 1, w: 1, n: 1, l: 1}. What is the expected number of occurrences of the pattern 'n*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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 1, k: 1, z: 2}, what is the expected number of times the pattern 'n.*z' 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 {r: 1, s: 1, x: 1, l: 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 1, n: 1, o: 1, w: 1}, what is the expected number of times the pattern 'nu*' 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 {y: 1, a: 2, i: 1}, 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": "0.67", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 1, m: 1, s: 1, f: 1}, 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {b: 1, w: 2, c: 1}. What is the expected number of occurrences of the pattern 'cb*' in 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 2 letters from the multiset {x: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {j: 1, r: 1, h: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'qr*'? 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 {t: 2, c: 1, d: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 2, g: 2}, what is the expected number of times the pattern 'g*f' appears? 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 2 letters from the multiset {x: 2, b: 2}. What is the expected number of occurrences of the pattern 'x.*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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {n: 1, j: 1, s: 1, e: 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {o: 3, d: 1}. What is the expected number of occurrences of the pattern 'o+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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {u: 1, t: 1, r: 2}. What is the expected number of occurrences of the pattern 'r.*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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {t: 1, h: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {d: 1, j: 1, y: 1, t: 1}. What is the expected number of occurrences of the pattern 'dt+' in 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": "When randomly selecting 2 letters from the multiset {m: 2, p: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'yp+'? 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 {w: 1, h: 2, n: 1}, what is the expected number of times the pattern 'h+w' 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 2 letters from the multiset {e: 1, c: 1, v: 2}. What is the expected number of occurrences of the pattern 'cv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {x: 2, h: 2}. What is the expected number of occurrences of the pattern 'h+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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {e: 1, i: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {v: 1, a: 1, y: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'ha*'? 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": "Form a word by randomly choosing 2 letters from the multiset {c: 1, q: 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 {e: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'e*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {v: 1, s: 2, d: 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {j: 3, 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 {w: 3, u: 1}. What is the expected number of occurrences of the pattern 'u.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {c: 1, z: 1, s: 1, m: 1}. What is the expected number of occurrences of the pattern 'c*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {h: 2, k: 2}. What is the expected number of occurrences of the pattern 'k.*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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {k: 3, w: 1}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 1, c: 1, k: 1, r: 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 2 letters from the multiset {y: 1, d: 1, k: 1, a: 1} 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {z: 1, e: 3} to form a word, what is the expected number of matches of the pattern 'z*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {h: 1, r: 1, e: 1, x: 1}. What is the expected number of occurrences of the pattern 'e*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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {x: 1, p: 2, h: 1}. What is the expected number of occurrences of the pattern 'h+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 {t: 3, c: 1}. What is the expected number of occurrences of the pattern 'tc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {l: 1, p: 1, g: 1, s: 1}. What is the expected number of occurrences of the pattern 'sg+' in 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": "When randomly selecting 2 letters from the multiset {o: 1, z: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'o+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": "When randomly selecting 2 letters from the multiset {q: 1, b: 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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {q: 1, g: 1, u: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'ug+'? 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 2 letters from the multiset {l: 1, z: 1, d: 1, s: 1}. 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {i: 1, b: 1, t: 1, p: 1}, what is the expected number of times the pattern 'p*b' 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": "Form a word by randomly choosing 2 letters from the multiset {y: 2, b: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {i: 1, u: 1, t: 1, m: 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": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 1, k: 2, w: 1}, what is the expected number of times the pattern 'w.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {n: 3, e: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {t: 1, y: 1, s: 1, e: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {j: 1, p: 3} to form a word, what is the expected number of matches of the pattern 'pj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {a: 1, s: 2, 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {x: 1, a: 1, j: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'zj*'? 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 {c: 1, t: 2, j: 1} 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {a: 1, w: 1, d: 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": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 3, w: 1}, what is the expected number of times the pattern 'wm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 2, f: 2}, what is the expected number of times the pattern 'gf*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {z: 3, g: 1} to form a word, what is the expected number of matches of the pattern 'z+g'? 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 {o: 1, y: 1, m: 2}, what is the expected number of times the pattern 'm+y' 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 2 by randomly selecting letters from the multiset {g: 1, c: 1, i: 1, p: 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {v: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {a: 1, i: 1, c: 1, s: 1}, what is the expected number of times the pattern 'ai*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 1, b: 1, l: 2}, what is the expected number of times the pattern 'l*b' appears? 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": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 1, f: 1, k: 1, i: 1}, what is the expected number of times the pattern 'v.*f' 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 2 letters from the multiset {t: 1, m: 1, c: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'g*t'? 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 {l: 1, q: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'l*p'? 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 {a: 1, z: 2, k: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 1, o: 1, m: 1, e: 1}, what is the expected number of times the pattern 'o+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 {x: 1, z: 1, f: 2}, what is the expected number of times the pattern 'zx+' 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 2 letters from the multiset {f: 1, h: 1, q: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {m: 2, k: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'x*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {d: 1, p: 1, s: 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": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 1, p: 2, e: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {n: 2, c: 2}. What is the expected number of occurrences of the pattern 'nc*' 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 2 by randomly selecting letters from the multiset {m: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {n: 1, w: 1, g: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'ng*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 1, k: 1, v: 2}, what is the expected number of times the pattern 'k*s' 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 {q: 2, 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {d: 1, n: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'd+w'? 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 {d: 2, e: 2} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {b: 1, e: 1, q: 1, j: 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 {p: 1, g: 1, e: 1, k: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {k: 2, j: 2}. What is the expected number of occurrences of the pattern 'kj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {g: 3, w: 1} to form a word, what is the expected number of matches of the pattern 'g*w'? 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 2 letters from the multiset {v: 1, k: 1, i: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'k+i'? 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 2 letters from the multiset {j: 2, n: 2}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 1, q: 2, r: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 2, 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {j: 1, e: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'l*e'? 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 2 letters from the multiset {b: 2, o: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {t: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 2, c: 1, a: 1}, what is the expected number of times the pattern 'c+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 1, r: 2, e: 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {p: 2, x: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'x+p'? 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 {e: 1, n: 1, m: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'n.*i'? 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: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'n+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {z: 1, k: 1, i: 2}. What is the expected number of occurrences of the pattern 'iz*' 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 2 by randomly selecting letters from the multiset {o: 1, n: 1, q: 1, z: 1}, 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {v: 1, q: 1, o: 1, d: 1}. What is the expected number of occurrences of the pattern 'vd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 1, k: 3}, what is the expected number of times the pattern 'hk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {q: 1, j: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'jc+'? 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 {p: 2, q: 2}, what is the expected number of times the pattern 'p*q' appears? 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 2 by randomly selecting letters from the multiset {u: 1, b: 3}, what is the expected number of times the pattern 'u.*b' 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 {k: 1, y: 3}, what is the expected number of times the pattern 'y+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": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 2, k: 2}, what is the expected number of times the pattern 'k.*o' 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": "Form a word by randomly choosing 2 letters from the multiset {w: 3, s: 1}. What is the expected number of occurrences of the pattern 'ws+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {n: 2, k: 1, u: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 2, a: 1, y: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {v: 1, w: 1, o: 2} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {w: 1, p: 1, m: 1, t: 1}. What is the expected number of occurrences of the pattern 'wp*' in 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 {o: 1, p: 1, x: 1, b: 1}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {i: 1, q: 3} to form a word, what is the expected number of matches of the pattern 'i*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {n: 1, d: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'n+e'? 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 2 letters from the multiset {n: 2, l: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {h: 3, d: 1}. What is the expected number of occurrences of the pattern 'd*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": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {w: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'wx*'? 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": "When randomly selecting 2 letters from the multiset {d: 1, p: 3} to form a word, what is the expected number of matches of the pattern 'pd+'? 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 {u: 2, v: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {m: 1, x: 1, z: 2}. What is the expected number of occurrences of the pattern 'm*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {d: 1, e: 2, g: 1}. What is the expected number of occurrences of the pattern 'g.*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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 2, x: 1, t: 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 2 letters from the multiset {m: 2, a: 1, h: 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": "Form a word by randomly choosing 2 letters from the multiset {p: 1, k: 1, d: 1, e: 1}. What is the expected number of occurrences of the pattern 'e*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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {o: 1, a: 1, w: 1, z: 1}. What is the expected number of occurrences of the pattern 'z+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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 1, n: 1, x: 1, j: 1}, what is the expected number of times the pattern 'js+' 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 2 letters from the multiset {x: 2, i: 1, b: 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": "Form a word by randomly choosing 2 letters from the multiset {l: 1, e: 1, w: 1, s: 1}. What is the expected number of occurrences of the pattern 'w.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {v: 1, c: 1, t: 1, l: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {x: 1, l: 1, n: 1, p: 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {x: 1, o: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'x+o'? 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 {n: 1, c: 1, t: 2}, what is the expected number of times the pattern 'n.*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": "When randomly selecting 2 letters from the multiset {f: 2, u: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'f.*u'? 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 {m: 3, o: 1}, what is the expected number of times the pattern 'om+' 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 {w: 1, i: 1, p: 1, o: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {c: 2, d: 1, h: 1}. What is the expected number of occurrences of the pattern 'd.*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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {f: 2, p: 1, x: 1}. What is the expected number of occurrences of the pattern 'p.*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": "When randomly selecting 2 letters from the multiset {l: 1, e: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'le*'? 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": "Form a word by randomly choosing 2 letters from the multiset {r: 1, j: 2, q: 1}. What is the expected number of occurrences of the pattern 'r*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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 2, f: 2}, 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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 1, y: 1, l: 2}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {u: 1, s: 1, q: 1, o: 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 {c: 1, x: 3} to form a word, what is the expected number of matches of the pattern 'xc+'? 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 {g: 3, b: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 1, q: 1, w: 2}, 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {u: 1, b: 3}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {d: 1, b: 1, y: 1, w: 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": "When randomly selecting 2 letters from the multiset {z: 1, e: 2, a: 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 2 letters from the multiset {q: 1, c: 1, j: 2}. What is the expected number of occurrences of the pattern 'c.*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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {s: 2, k: 1, u: 1}. What is the expected number of occurrences of the pattern 'sk*' 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": "When randomly selecting 2 letters from the multiset {o: 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": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 2, t: 2}, what is the expected number of times the pattern 'dt*' appears? 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 2 by randomly selecting letters from the multiset {q: 1, i: 1, b: 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": "0.67", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 3, d: 1}, what is the expected number of times the pattern 'dp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {t: 2, q: 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 2 by randomly selecting letters from the multiset {r: 2, m: 2}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {x: 1, t: 2, c: 1} to form a word, what is the expected number of matches of the pattern 'c*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {p: 1, c: 1, q: 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 {d: 1, m: 1, c: 1, z: 1}, what is the expected number of times the pattern 'd+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": "If you form a word of length 2 by randomly selecting letters from the multiset {l: 2, s: 1, h: 1}, what is the expected number of times the pattern 'sl+' 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 {h: 1, o: 3} to form a word, what is the expected number of matches of the pattern 'o+h'? 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 {b: 1, o: 1, m: 1, q: 1}. What is the expected number of occurrences of the pattern 'mb*' in 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 {t: 1, s: 3}. What is the expected number of occurrences of the pattern 'st*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {k: 1, e: 1, z: 2}, what is the expected number of times the pattern 'e+k' 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 2 letters from the multiset {t: 2, d: 2}. What is the expected number of occurrences of the pattern 'dt*' 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": "Form a word by randomly choosing 2 letters from the multiset {h: 1, w: 1, g: 2}. What is the expected number of occurrences of the pattern 'w.*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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 2, s: 1, o: 1}, what is the expected number of times the pattern 'g.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 1, c: 1, h: 1, a: 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {m: 2, z: 1, u: 1}. What is the expected number of occurrences of the pattern 'zm*' in 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 2 letters from the multiset {x: 1, n: 2, c: 1}. What is the expected number of occurrences of the pattern 'n+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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {y: 1, z: 1, w: 2}. What is the expected number of occurrences of the pattern 'wz+' in 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 {q: 3, y: 1}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {n: 1, k: 1, f: 1, v: 1}. What is the expected number of occurrences of the pattern 'nv*' in 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 {y: 1, q: 2, r: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {j: 2, i: 1, z: 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {x: 2, f: 1, b: 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": "Form a word by randomly choosing 2 letters from the multiset {q: 1, y: 1, v: 1, t: 1}. What is the expected number of occurrences of the pattern 't+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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {e: 1, x: 1, y: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 1, c: 1, n: 2}, 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": "0.67", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {o: 2, x: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'o*e'? 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 {h: 1, e: 1, o: 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 2 letters from the multiset {q: 1, c: 1, y: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 1, c: 1, t: 1, k: 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 2 by randomly selecting letters from the multiset {t: 2, z: 1, q: 1}, what is the expected number of times the pattern 't*q' appears? 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": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 2, f: 1, j: 1}, what is the expected number of times the pattern 'j+c' 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 {x: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'x.*o'? 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: 2, q: 1, p: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {d: 1, a: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'a*c'? 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 2 letters from the multiset {c: 1, e: 1, i: 1, h: 1}. What is the expected number of occurrences of the pattern 'e+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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {b: 1, r: 1, a: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'zr*'? 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 {z: 1, k: 3} to form a word, what is the expected number of matches of the pattern 'zk+'? 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 {i: 1, h: 1, b: 1, d: 1}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {g: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'g*p'? 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 2 by randomly selecting letters from the multiset {c: 1, x: 2, v: 1}, what is the expected number of times the pattern 'vc+' 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 2 letters from the multiset {h: 2, f: 2}. What is the expected number of occurrences of the pattern 'f.*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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 2, k: 2}, what is the expected number of times the pattern 'kf+' 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 {t: 2, j: 2} to form a word, what is the expected number of matches of the pattern 'tj+'? 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 {s: 1, j: 2, r: 1}, 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {j: 1, s: 2, y: 1}, what is the expected number of times the pattern 'sj+' 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 2 letters from the multiset {i: 1, y: 1, w: 1, p: 1}. What is the expected number of occurrences of the pattern 'wi*' in 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": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 2, l: 2}, what is the expected number of times the pattern 'd*l' appears? 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 2 letters from the multiset {n: 3, a: 1}. What is the expected number of occurrences of the pattern 'a+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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {q: 2, 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {b: 2, p: 1, f: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {t: 1, r: 1, g: 2}. What is the expected number of occurrences of the pattern 'g*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": "0.67", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {w: 2, b: 2}. What is the expected number of occurrences of the pattern 'w.*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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {h: 1, l: 3}. What is the expected number of occurrences of the pattern 'h.*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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {v: 2, p: 2}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {x: 2, i: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {w: 2, l: 1, o: 1}. What is the expected number of occurrences of the pattern 'w.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {s: 1, p: 1, y: 1, u: 1}. What is the expected number of occurrences of the pattern 's*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 1, u: 3}, what is the expected number of times the pattern 'x*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {n: 1, l: 2, t: 1}. What is the expected number of occurrences of the pattern 'ln+' in 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 {f: 1, m: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'uf+'? 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 {i: 1, j: 3}, 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {u: 2, b: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {d: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'dn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {e: 1, z: 1, j: 1, b: 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 2 by randomly selecting letters from the multiset {b: 3, h: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 2, y: 1, o: 1}, what is the expected number of times the pattern 'y.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {u: 1, 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {p: 3, z: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {i: 3, 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": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {g: 3, t: 1} to form a word, what is the expected number of matches of the pattern 'tg+'? 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 {r: 1, b: 1, k: 1, v: 1}, what is the expected number of times the pattern 'vv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {r: 1, b: 3} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {w: 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 {h: 1, n: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {h: 2, o: 2}. What is the expected number of occurrences of the pattern 'o*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {o: 1, p: 1, q: 2}. What is the expected number of occurrences of the pattern 'q+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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 2, e: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {a: 1, l: 1, 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {t: 1, d: 1, r: 1, q: 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 2 letters from the multiset {z: 1, e: 3}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {c: 1, r: 1, x: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'r.*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": "When randomly selecting 2 letters from the multiset {p: 1, h: 1, c: 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": "Form a word by randomly choosing 2 letters from the multiset {j: 1, o: 1, i: 1, n: 1}. What is the expected number of occurrences of the pattern 'j+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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {p: 2, m: 1, a: 1} 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {l: 2, j: 2}, what is the expected number of times the pattern 'j*l' appears? 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": "When randomly selecting 2 letters from the multiset {h: 1, i: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {n: 1, q: 1, s: 1, j: 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 1, w: 2, f: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {p: 1, f: 3}. What is the expected number of occurrences of the pattern 'p*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 1, j: 1, b: 2}, what is the expected number of times the pattern 'yb+' 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 2 letters from the multiset {j: 2, s: 2}. 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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {v: 1, x: 1, e: 1, q: 1}. What is the expected number of occurrences of the pattern 'x.*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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {i: 2, q: 2}. What is the expected number of occurrences of the pattern 'q.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {l: 1, w: 3}, what is the expected number of times the pattern 'l*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 3, o: 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": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {y: 1, a: 3}. What is the expected number of occurrences of the pattern 'a*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {i: 1, p: 2, b: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {f: 1, z: 1, a: 2} 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {h: 2, f: 2} 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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {u: 1, a: 1, m: 1, y: 1}. What is the expected number of occurrences of the pattern 'my*' in 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 {r: 1, e: 2, i: 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": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 1, n: 3}, what is the expected number of times the pattern 'n*v' 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 {s: 3, f: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {u: 1, h: 1, w: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'w*h'? 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 {v: 1, l: 1, a: 1, x: 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 2 letters from the multiset {f: 2, x: 2}. What is the expected number of occurrences of the pattern 'f*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": "1.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {j: 1, e: 1, q: 2} 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 1, c: 1, j: 1, i: 1}, what is the expected number of times the pattern 'o+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {l: 2, f: 2}. What is the expected number of occurrences of the pattern 'f.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {s: 2, g: 2}. What is the expected number of occurrences of the pattern 's.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {i: 2, o: 1, c: 1}. What is the expected number of occurrences of the pattern 'io+' in 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 {l: 3, 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": "If you form a word of length 2 by randomly selecting letters from the multiset {b: 1, i: 1, y: 1, a: 1}, what is the expected number of times the pattern 'yi+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {k: 1, h: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'k*h'? 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 {c: 1, f: 3}, what is the expected number of times the pattern 'cf+' 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 {y: 1, s: 1, w: 1, r: 1}, what is the expected number of times the pattern 'wy*' 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": "Form a word by randomly choosing 2 letters from the multiset {l: 1, e: 1, c: 1, n: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 3, 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": "Form a word by randomly choosing 2 letters from the multiset {e: 1, q: 1, m: 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 2 letters from the multiset {k: 2, b: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 2, c: 2}, what is the expected number of times the pattern 'c+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {l: 2, v: 1, g: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {o: 1, t: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'o*t'? 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": "Form a word by randomly choosing 2 letters from the multiset {f: 2, h: 1, u: 1}. What is the expected number of occurrences of the pattern 'uf*' in 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": "If you form a word of length 2 by randomly selecting letters from the multiset {b: 1, j: 1, i: 1, r: 1}, what is the expected number of times the pattern 'rb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 1, c: 3}, what is the expected number of times the pattern 'rc*' 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 2 by randomly selecting letters from the multiset {k: 2, q: 2}, 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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 1, c: 2, i: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {c: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'cu*'? 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": "When randomly selecting 2 letters from the multiset {b: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'd.*b'? 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 {e: 2, t: 1, r: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {v: 2, s: 1, u: 1}. What is the expected number of occurrences of the pattern 'v.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 2, e: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {w: 1, r: 1, g: 1, k: 1}. What is the expected number of occurrences of the pattern 'r*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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 1, z: 1, i: 1, o: 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": "Form a word by randomly choosing 2 letters from the multiset {e: 1, m: 1, x: 2}. What is the expected number of occurrences of the pattern 'xe+' in 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 {p: 1, h: 1, l: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'l.*h'? 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 2 letters from the multiset {y: 2, o: 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": "1.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 1, h: 1, l: 1, m: 1}, what is the expected number of times the pattern 'h+t' 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 2 letters from the multiset {d: 1, x: 2, i: 1}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 1, p: 3}, 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {s: 2, z: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {q: 1, f: 1, x: 1, a: 1}. What is the expected number of occurrences of the pattern 'x+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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {p: 2, n: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'p.*n'? 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 {j: 3, f: 1}, what is the expected number of times the pattern 'jf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {e: 1, 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {t: 1, p: 1, k: 2}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {n: 1, l: 1, p: 1, t: 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {z: 3, a: 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": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {t: 1, c: 1, x: 2}. What is the expected number of occurrences of the pattern 'x*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": "0.67", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 1, m: 1, c: 1, o: 1}, what is the expected number of times the pattern 't+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": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 2, w: 2}, what is the expected number of times the pattern 'e*w' appears? 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 2 by randomly selecting letters from the multiset {c: 2, v: 2}, what is the expected number of times the pattern 'vc*' appears? 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": "When randomly selecting 2 letters from the multiset {r: 3, w: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {g: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'ag+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 1, o: 1, p: 1, x: 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": "When randomly selecting 2 letters from the multiset {e: 1, s: 1, q: 1, c: 1} to form a word, what is the expected number of matches of the pattern 's.*q'? 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 2 letters from the multiset {l: 1, p: 1, u: 1, q: 1}. What is the expected number of occurrences of the pattern 'lq*' in 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 2 letters from the multiset {d: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'd.*n'? 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 {c: 1, l: 1, f: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'o+c'? 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 2 letters from the multiset {p: 2, t: 1, q: 1}. What is the expected number of occurrences of the pattern 'q.*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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {l: 2, r: 1, z: 1}, what is the expected number of times the pattern 'r*z' 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": "Form a word by randomly choosing 2 letters from the multiset {c: 1, g: 1, x: 1, y: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {b: 1, h: 1, a: 1, p: 1}, what is the expected number of times the pattern 'a.*h' 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 2 letters from the multiset {v: 2, q: 2} 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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 1, s: 1, f: 1, j: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 1, p: 1, i: 1, o: 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 2 letters from the multiset {h: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'hb*'? 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": "When randomly selecting 2 letters from the multiset {f: 1, r: 3} to form a word, what is the expected number of matches of the pattern 'r+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {u: 3, l: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {g: 1, w: 1, a: 1, 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 1, a: 1, e: 1, g: 1}, what is the expected number of times the pattern 'gu*' 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": "Form a word by randomly choosing 2 letters from the multiset {r: 1, s: 1, d: 2}. What is the expected number of occurrences of the pattern 'd+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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {j: 1, d: 2, q: 1}, what is the expected number of times the pattern 'j+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {y: 1, u: 1, x: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'l*x'? 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 {c: 2, i: 1, m: 1}, what is the expected number of times the pattern 'c*m' appears? 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": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 1, j: 1, m: 1, k: 1}, what is the expected number of times the pattern 'k+y' 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 2 letters from the multiset {s: 1, e: 1, k: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'k*e'? 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": "Form a word by randomly choosing 2 letters from the multiset {t: 2, 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {l: 2, n: 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": "Form a word by randomly choosing 2 letters from the multiset {s: 1, r: 1, j: 1, m: 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 2, p: 2}, what is the expected number of times the pattern 'py*' appears? 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 2 by randomly selecting letters from the multiset {y: 1, n: 1, z: 1, x: 1}, what is the expected number of times the pattern 'y+x' 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 2 letters from the multiset {t: 1, u: 3}. What is the expected number of occurrences of the pattern 't.*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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {m: 2, h: 2}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {e: 2, s: 1, x: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {c: 1, g: 1, b: 1, w: 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {s: 2, o: 1, p: 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 {y: 2, g: 2}. What is the expected number of occurrences of the pattern 'g+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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {e: 1, y: 3}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 1, v: 2, e: 1}, what is the expected number of times the pattern 'q*v' 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 {x: 2, h: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'xs+'? 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, h: 3}. 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": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {s: 1, d: 1, a: 2}. What is the expected number of occurrences of the pattern 'd.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {v: 1, q: 1, y: 1, f: 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 1, c: 3}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {u: 1, v: 1, m: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {t: 2, 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 2, g: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {k: 2, j: 2}. 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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {e: 2, q: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'zq*'? 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 {j: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'j.*p'? 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 {f: 1, 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 3, u: 1}, what is the expected number of times the pattern 'eu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 1, l: 1, a: 1, i: 1}, what is the expected number of times the pattern 'al+' 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 2 letters from the multiset {j: 1, e: 1, o: 1, h: 1}. What is the expected number of occurrences of the pattern 'o+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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 1, q: 1, i: 1, r: 1}, what is the expected number of times the pattern 'iq+' 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 2 letters from the multiset {s: 1, h: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'sd+'? 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 {i: 1, t: 1, c: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'i*t'? 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 {o: 2, s: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'o*s'? 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": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 1, n: 2, 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": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 1, e: 1, z: 1, b: 1}, what is the expected number of times the pattern 'e*t' 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 {o: 3, y: 1}, what is the expected number of times the pattern 'oy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 1, f: 1, z: 1, q: 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": "When randomly selecting 2 letters from the multiset {i: 1, d: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'd+i'? 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 {j: 1, f: 1, b: 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": "Form a word by randomly choosing 2 letters from the multiset {r: 1, k: 3}. What is the expected number of occurrences of the pattern 'rk+' in 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": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 2, d: 1, h: 1}, what is the expected number of times the pattern 'nh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {q: 1, e: 1, h: 1, m: 1} 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {p: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'xp*'? 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": "When randomly selecting 2 letters from the multiset {x: 1, w: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'x.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {j: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'd+j'? 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 {y: 1, k: 1, e: 2}. What is the expected number of occurrences of the pattern 'ye*' in 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 2 letters from the multiset {g: 1, k: 1, d: 1, s: 1}. What is the expected number of occurrences of the pattern 'g.*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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {z: 1, e: 3}, what is the expected number of times the pattern 'e+z' 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 {t: 1, l: 1, p: 2}. 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {b: 2, x: 1, o: 1}. What is the expected number of occurrences of the pattern 'x*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {u: 1, o: 1, f: 1, p: 1}. What is the expected number of occurrences of the pattern 'f*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 1, t: 1, g: 1, k: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {v: 3, l: 1} 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": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {c: 2, i: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'z.*i'? 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 {j: 1, t: 1, o: 1, h: 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 2 letters from the multiset {u: 1, s: 1, g: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'su*'? 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 {c: 1, g: 2, t: 1}, what is the expected number of times the pattern 't.*g' 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 2 by randomly selecting letters from the multiset {r: 1, e: 3}, what is the expected number of times the pattern 're+' 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 {z: 1, g: 3}, what is the expected number of times the pattern 'zg+' 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, c: 2, u: 1}, what is the expected number of times the pattern 'ci*' 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 {e: 1, n: 1, k: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'j+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {e: 3, g: 1} to form a word, what is the expected number of matches of the pattern 'ge*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {i: 1, a: 1, d: 1, b: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 1, z: 1, u: 1, k: 1}, what is the expected number of times the pattern 'k+z' 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 {c: 1, g: 1, p: 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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {s: 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": "Form a word by randomly choosing 2 letters from the multiset {m: 1, v: 1, o: 1, g: 1}. What is the expected number of occurrences of the pattern 'o.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 2, h: 2}, what is the expected number of times the pattern 'h.*t' 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 {v: 1, l: 1, 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 1, p: 2, r: 1}, what is the expected number of times the pattern 'pr*' 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": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 1, q: 2, l: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {l: 1, o: 1, a: 1, x: 1}, what is the expected number of times the pattern 'a+o' 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 2 letters from the multiset {y: 1, l: 1, q: 2}. What is the expected number of occurrences of the pattern 'y*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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {v: 2, m: 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 2 by randomly selecting letters from the multiset {a: 1, n: 1, w: 1, y: 1}, what is the expected number of times the pattern 'wn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {h: 2, f: 2}. What is the expected number of occurrences of the pattern 'f.*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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {t: 1, m: 1, z: 1, k: 1}. What is the expected number of occurrences of the pattern 'm.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 1, s: 1, e: 1, 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {k: 1, n: 2, s: 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": "When randomly selecting 2 letters from the multiset {f: 1, d: 2, c: 1} to form a word, what is the expected number of matches of the pattern 'f.*d'? 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 {a: 1, e: 2, p: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 1, a: 1, b: 1, s: 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, a: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {a: 1, g: 2, q: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {x: 1, i: 3}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {k: 2, u: 2}. What is the expected number of occurrences of the pattern 'k*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": "1.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {w: 1, q: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'q.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 2, h: 1, y: 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": "Form a word by randomly choosing 2 letters from the multiset {k: 1, x: 1, f: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 1, a: 3}, what is the expected number of times the pattern 'd+a' 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 {v: 2, n: 2}, what is the expected number of times the pattern 'nv+' 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": "Form a word by randomly choosing 2 letters from the multiset {u: 2, c: 2}. What is the expected number of occurrences of the pattern 'u.*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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 1, f: 1, t: 1, k: 1}, what is the expected number of times the pattern 'k*t' 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": "When randomly selecting 2 letters from the multiset {g: 1, v: 1, a: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'vi+'? 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 {g: 2, f: 1, i: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {x: 1, b: 1, o: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'xb*'? 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 {u: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'lu+'? 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 {w: 1, a: 1, v: 1, e: 1} 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {g: 3, z: 1} to form a word, what is the expected number of matches of the pattern 'zg*'? 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 2 letters from the multiset {k: 1, i: 1, s: 1, q: 1} to form a word, what is the expected number of matches of the pattern 's.*q'? 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 2 letters from the multiset {l: 1, o: 2, k: 1}. What is the expected number of occurrences of the pattern 'o*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": "0.67", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 1, y: 1, p: 1, o: 1}, what is the expected number of times the pattern 'ys+' 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, m: 2}, what is the expected number of times the pattern 'mu*' appears? 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 2 by randomly selecting letters from the multiset {k: 1, s: 1, o: 1, i: 1}, 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {q: 1, d: 2, b: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 3, h: 1}, what is the expected number of times the pattern 'h+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": "Form a word by randomly choosing 2 letters from the multiset {g: 1, y: 2, m: 1}. What is the expected number of occurrences of the pattern 'm*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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 3, q: 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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 1, v: 2, h: 1}, what is the expected number of times the pattern 'gh*' 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": "Form a word by randomly choosing 2 letters from the multiset {h: 1, t: 1, r: 1, p: 1}. What is the expected number of occurrences of the pattern 'pr+' in 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": "When randomly selecting 2 letters from the multiset {d: 1, a: 2, s: 1} to form a word, what is the expected number of matches of the pattern 's+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {c: 1, a: 1, b: 1, q: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {m: 1, c: 3} to form a word, what is the expected number of matches of the pattern 'cm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {d: 1, v: 3}. What is the expected number of occurrences of the pattern 'dv*' in 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 2 letters from the multiset {r: 1, i: 3} to form a word, what is the expected number of matches of the pattern 'ri+'? 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 {l: 2, o: 1, b: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 1, h: 1, q: 2}, what is the expected number of times the pattern 'h.*q' 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 {m: 1, w: 2, s: 1} to form a word, what is the expected number of matches of the pattern 's+w'? 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 {z: 2, e: 2}, what is the expected number of times the pattern 'e.*z' 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 {n: 1, i: 1, w: 1, s: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 3, g: 1}, what is the expected number of times the pattern 'c.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {o: 1, z: 1, n: 1, j: 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 2 by randomly selecting letters from the multiset {b: 2, e: 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": "1.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {b: 1, z: 1, t: 1, i: 1}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 1, d: 1, o: 2}, 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {b: 1, y: 1, d: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'd*z'? 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 {h: 3, 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 2 by randomly selecting letters from the multiset {h: 2, k: 2}, what is the expected number of times the pattern 'hk+' 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 {n: 1, c: 3}, what is the expected number of times the pattern 'cn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {o: 1, w: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'l.*o'? 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 {p: 1, s: 2, b: 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 2 by randomly selecting letters from the multiset {a: 1, j: 1, i: 1, e: 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 2 by randomly selecting letters from the multiset {z: 1, e: 1, q: 1, d: 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 2 by randomly selecting letters from the multiset {g: 1, m: 1, z: 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": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 1, j: 1, y: 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 2 by randomly selecting letters from the multiset {k: 1, h: 1, v: 1, j: 1}, what is the expected number of times the pattern 'kh+' 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 2 letters from the multiset {i: 1, j: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'a.*i'? 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 {z: 1, x: 1, u: 2} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {r: 1, j: 2, k: 1}. What is the expected number of occurrences of the pattern 'jr*' 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 2 by randomly selecting letters from the multiset {m: 2, j: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {n: 2, t: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 1, x: 1, v: 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 2 by randomly selecting letters from the multiset {a: 1, u: 1, b: 1, d: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {o: 2, p: 1, w: 1}. What is the expected number of occurrences of the pattern 'w+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": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {m: 2, z: 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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {v: 1, c: 1, z: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'pz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {z: 2, o: 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 2 letters from the multiset {b: 2, k: 1, t: 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {l: 1, v: 1, d: 1, z: 1}, what is the expected number of times the pattern 'dz*' 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 {o: 1, r: 1, y: 1, j: 1}, what is the expected number of times the pattern 'r*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {p: 3, l: 1} to form a word, what is the expected number of matches of the pattern 'p+l'? 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, r: 2, k: 1}, what is the expected number of times the pattern 'e.*k' 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 2 letters from the multiset {o: 1, b: 1, q: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'oo*'? 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 {g: 2, o: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 1, x: 1, z: 1, s: 1}, what is the expected number of times the pattern 'zs+' 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 2 letters from the multiset {b: 1, i: 2, u: 1}. What is the expected number of occurrences of the pattern 'u.*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 {x: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'x.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 1, f: 1, s: 2}, what is the expected number of times the pattern 'mf+' 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 2 letters from the multiset {s: 1, r: 1, a: 1, b: 1} to form a word, what is the expected number of matches of the pattern 's*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {m: 1, v: 1, z: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'vz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 1, x: 1, v: 1, f: 1}, what is the expected number of times the pattern 'g*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {t: 2, w: 2}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 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": "Form a word by randomly choosing 2 letters from the multiset {c: 2, z: 2}. What is the expected number of occurrences of the pattern 'c+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {t: 1, p: 1, o: 1, d: 1} 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": "0.58", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 3, x: 1}, what is the expected number of times the pattern 'x.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 1, u: 1, v: 1, l: 1}, what is the expected number of times the pattern 'l*u' 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 {b: 2, v: 2}, 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": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 1, s: 1, g: 1, q: 1}, what is the expected number of times the pattern 'g.*q' 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 2 letters from the multiset {f: 1, x: 3}. What is the expected number of occurrences of the pattern 'fx*' in 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 {s: 1, m: 1, c: 1, n: 1}. What is the expected number of occurrences of the pattern 'mc*' in 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": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 3, i: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 3, a: 1}, 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": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {e: 1, q: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'x*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.67", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {b: 2, m: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {d: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'e.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {b: 1, x: 1, j: 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": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 1, m: 1, l: 1, n: 1}, what is the expected number of times the pattern 'gn+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.08", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {o: 2, t: 2}. What is the expected number of occurrences of the pattern 'ot+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {i: 2, g: 1, m: 1}. What is the expected number of occurrences of the pattern 'mi*' in 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": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 3, 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": "0.5", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {o: 1, b: 1, r: 1, d: 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": "When randomly selecting 2 letters from the multiset {u: 1, t: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'ue*'? 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": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 1, z: 2, p: 1}, 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {z: 1, i: 3}. What is the expected number of occurrences of the pattern 'z.*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": "0.25", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {e: 1, i: 1, o: 1, c: 1}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {f: 1, i: 1, n: 1, p: 1}. What is the expected number of occurrences of the pattern 'fn*' in 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": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 1, p: 1, v: 1, u: 1}, what is the expected number of times the pattern 'uh*' 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": "When randomly selecting 2 letters from the multiset {i: 1, k: 1, l: 1, a: 1} to form a word, what is the expected number of matches of the pattern 'li+'? 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 {q: 1, o: 2, g: 1} to form a word, what is the expected number of matches of the pattern 'g.*o'? 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 {b: 1, u: 1, e: 1, y: 1}, what is the expected number of times the pattern 'y.*b' 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 {b: 1, v: 1, q: 1, 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": "Form a word by randomly choosing 2 letters from the multiset {w: 2, m: 2}. What is the expected number of occurrences of the pattern 'm.*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": "0.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 3, n: 1}, what is the expected number of times the pattern 'nt*' 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 2 by randomly selecting letters from the multiset {e: 3, z: 1}, 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": "1.75", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 1, h: 3}, what is the expected number of times the pattern 'h*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.75", "dataset": "MATH"}
+{"messages": [{"content": "When randomly selecting 2 letters from the multiset {d: 1, h: 1, p: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {k: 1, w: 1, j: 1, l: 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": "When randomly selecting 2 letters from the multiset {f: 2, s: 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": "0.17", "dataset": "MATH"}
+{"messages": [{"content": "Form a word by randomly choosing 2 letters from the multiset {t: 2, q: 2}. What is the expected number of occurrences of the pattern 'q*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": "1.33", "dataset": "MATH"}
+{"messages": [{"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 1, m: 1, c: 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 {z: 1, s: 1, b: 1, g: 1}, what is the expected number of times the pattern 's*z' 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 {q: 2, m: 1, s: 1}, what is the expected number of times the pattern 'q.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.17", "dataset": "MATH"}