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data.jsonl
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| 1 |
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{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, a: 3, b: 4, c: 1, o: 2}, what is the expected number of times the pattern 'r.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
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| 2 |
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{"messages": [{"content": "When randomly selecting 3 letters from the multiset {j: 1, w: 5, z: 2, g: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
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| 3 |
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{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 3, g: 2, s: 1, q: 2, o: 2}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
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| 4 |
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{"messages": [{"content": "When randomly selecting 3 letters from the multiset {x: 3, p: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'hp+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.27", "dataset": "MATH"}
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| 5 |
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{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, m: 2, h: 3, c: 5}. What is the expected number of occurrences of the pattern 'pm+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.04", "dataset": "MATH"}
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| 6 |
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{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 3, a: 2, o: 3, v: 1, h: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
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| 7 |
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{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 2, i: 6}, what is the expected number of times the pattern 'y*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.71", "dataset": "MATH"}
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| 8 |
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{"messages": [{"content": "When randomly selecting 4 letters from the multiset {m: 4, b: 4, 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": "1.27", "dataset": "MATH"}
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| 9 |
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{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, y: 4, g: 1, q: 3, p: 2}. What is the expected number of occurrences of the pattern 'pc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.58", "dataset": "MATH"}
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| 10 |
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{"messages": [{"content": "When randomly selecting 3 letters from the multiset {s: 4, o: 3, h: 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": "0.3", "dataset": "MATH"}
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| 11 |
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{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, y: 9}. What is the expected number of occurrences of the pattern 'yq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.35", "dataset": "MATH"}
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| 12 |
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{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, x: 2, a: 4, h: 4}, what is the expected number of times the pattern 'ra+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.14", "dataset": "MATH"}
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| 13 |
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{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, s: 3, g: 3}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
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| 14 |
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{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, w: 3, q: 2, l: 2}, what is the expected number of times the pattern 'x*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.82", "dataset": "MATH"}
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| 15 |
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{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 4, w: 6} to form a word, what is the expected number of matches of the pattern 'h*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.43", "dataset": "MATH"}
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| 16 |
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{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, l: 4, s: 4}, 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": "0.16", "dataset": "MATH"}
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| 17 |
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{"messages": [{"content": "When randomly selecting 3 letters from the multiset {f: 4, i: 5, x: 2} to form a word, what is the expected number of matches of the pattern 'xi+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
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| 18 |
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{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {z: 4, m: 2, b: 5}. What is the expected number of occurrences of the pattern 'z*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.83", "dataset": "MATH"}
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| 19 |
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{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, v: 3, c: 1, p: 3, s: 3}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.16", "dataset": "MATH"}
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| 20 |
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{"messages": [{"content": "When randomly selecting 4 letters from the multiset {a: 4, d: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'da+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
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| 21 |
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{"messages": [{"content": "When randomly selecting 4 letters from the multiset {l: 5, e: 3} 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": "1.27", "dataset": "MATH"}
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| 22 |
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{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, m: 3, u: 4}, what is the expected number of times the pattern 'm.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
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| 23 |
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{"messages": [{"content": "When randomly selecting 3 letters from the multiset {c: 2, m: 2, q: 2, d: 1, w: 2} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
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| 24 |
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{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 2, g: 4, l: 2, i: 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": "0.07", "dataset": "MATH"}
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| 25 |
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{"messages": [{"content": "Form a word by randomly choosing 3 letters from the multiset {t: 7, r: 5}. What is the expected number of occurrences of the pattern 't+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.69", "dataset": "MATH"}
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| 26 |
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{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 4, k: 4}, what is the expected number of times the pattern 'v*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.21", "dataset": "MATH"}
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| 27 |
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{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, q: 8}, what is the expected number of times the pattern 'q+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.51", "dataset": "MATH"}
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| 28 |
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{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, u: 2, s: 1, g: 3, i: 2}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.07", "dataset": "MATH"}
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| 29 |
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{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 3, v: 4, z: 2, b: 2} 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": "0.15", "dataset": "MATH"}
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| 30 |
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{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 5, g: 4, k: 3} to form a word, what is the expected number of matches of the pattern 'kp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.02", "dataset": "MATH"}
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| 31 |
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{"messages": [{"content": "When randomly selecting 3 letters from the multiset {u: 2, c: 2, f: 2, o: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'on+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.04", "dataset": "MATH"}
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| 32 |
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{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 3, h: 3, f: 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": "0.64", "dataset": "MATH"}
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| 33 |
+
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {e: 7, w: 2} to form a word, what is the expected number of matches of the pattern 'w.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.17", "dataset": "MATH"}
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| 34 |
+
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 4, f: 7}, 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": "0.65", "dataset": "MATH"}
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| 35 |
+
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {e: 5, w: 4} to form a word, what is the expected number of matches of the pattern 'w.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.83", "dataset": "MATH"}
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| 36 |
+
{"messages": [{"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, j: 4, a: 2, h: 1}, what is the expected number of times the pattern 'na*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.79", "dataset": "MATH"}
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| 37 |
+
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {u: 2, f: 2, n: 3, c: 2} 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": "0.18", "dataset": "MATH"}
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| 38 |
+
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {t: 3, x: 1, y: 4, r: 2} to form a word, what is the expected number of matches of the pattern 'r*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.89", "dataset": "MATH"}
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| 39 |
+
{"messages": [{"content": "When randomly selecting 3 letters from the multiset {p: 4, u: 3, l: 2} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.25", "dataset": "MATH"}
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| 40 |
+
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 1, f: 2, u: 1, e: 3, r: 2}. What is the expected number of occurrences of the pattern 'e*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.19", "dataset": "MATH"}
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| 41 |
+
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 4, r: 4, z: 6} to form a word, what is the expected number of matches of the pattern 'rj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.45", "dataset": "MATH"}
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| 42 |
+
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 1, p: 5, l: 8}, 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": "3.22", "dataset": "MATH"}
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| 43 |
+
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {f: 3, p: 3, b: 4}. 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": "0.29", "dataset": "MATH"}
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| 44 |
+
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {c: 3, r: 7}. 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": "3.29", "dataset": "MATH"}
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| 45 |
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{"messages": [{"content": "When randomly selecting 4 letters from the multiset {p: 3, y: 2, b: 3, h: 7} to form a word, what is the expected number of matches of the pattern 'hh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.65", "dataset": "MATH"}
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| 46 |
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{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 4, q: 3, k: 3, 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": "0.23", "dataset": "MATH"}
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| 47 |
+
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {y: 2, v: 2, l: 4, k: 2, h: 3} to form a word, what is the expected number of matches of the pattern 'ky+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.11", "dataset": "MATH"}
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| 48 |
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{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 7, i: 4, b: 3}, 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": "0.3", "dataset": "MATH"}
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| 49 |
+
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 7, z: 2, p: 3}, 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": "1.06", "dataset": "MATH"}
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| 50 |
+
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 4, n: 3, g: 3}, what is the expected number of times the pattern 'pn*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.64", "dataset": "MATH"}
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| 51 |
+
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {h: 4, c: 2, o: 5, a: 4} 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": "0.57", "dataset": "MATH"}
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| 52 |
+
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {h: 1, l: 5, n: 3, x: 3, y: 3}. What is the expected number of occurrences of the pattern 'l*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.45", "dataset": "MATH"}
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| 53 |
+
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {d: 4, h: 5, t: 5}. What is the expected number of occurrences of the pattern 't.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
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| 54 |
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{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 6, h: 7}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.62", "dataset": "MATH"}
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| 55 |
+
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {i: 5, x: 10}. What is the expected number of occurrences of the pattern 'x+i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.15", "dataset": "MATH"}
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| 56 |
+
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {b: 3, s: 3, l: 3, k: 3, 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": "0.11", "dataset": "MATH"}
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| 57 |
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{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 3, o: 5, u: 5}, what is the expected number of times the pattern 'o.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
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| 58 |
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{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 5, h: 5, o: 5}, what is the expected number of times the pattern 'x.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.71", "dataset": "MATH"}
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| 59 |
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{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 3, m: 7} to form a word, what is the expected number of matches of the pattern 'xm*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.38", "dataset": "MATH"}
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| 60 |
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{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {g: 6, l: 6}. 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": "1.36", "dataset": "MATH"}
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| 61 |
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{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, w: 1, o: 2, z: 3, e: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
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| 62 |
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{"messages": [{"content": "When randomly selecting 4 letters from the multiset {e: 9, l: 4} to form a word, what is the expected number of matches of the pattern 'e+l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.15", "dataset": "MATH"}
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| 63 |
+
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {d: 4, i: 4, n: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
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| 64 |
+
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {x: 6, y: 6} to form a word, what is the expected number of matches of the pattern 'xy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.15", "dataset": "MATH"}
|
| 65 |
+
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {f: 5, w: 5} to form a word, what is the expected number of matches of the pattern 'wf+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.67", "dataset": "MATH"}
|
| 66 |
+
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 7, g: 3}, 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": "1.4", "dataset": "MATH"}
|
| 67 |
+
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 7, m: 3}, what is the expected number of times the pattern 'mp+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.79", "dataset": "MATH"}
|
| 68 |
+
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {c: 5, i: 6, h: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.15", "dataset": "MATH"}
|
| 69 |
+
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 3, t: 4, m: 1, z: 1, p: 3}, what is the expected number of times the pattern 'o*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.57", "dataset": "MATH"}
|
| 70 |
+
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 2, j: 8}, what is the expected number of times the pattern 'ij+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.98", "dataset": "MATH"}
|
| 71 |
+
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {r: 5, a: 5}. What is the expected number of occurrences of the pattern 'ar+' 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"}
|
| 72 |
+
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 9, d: 6}, what is the expected number of times the pattern 'dc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.74", "dataset": "MATH"}
|
| 73 |
+
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {d: 4, m: 4, y: 3}. What is the expected number of occurrences of the pattern 'm.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.87", "dataset": "MATH"}
|
| 74 |
+
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 3, j: 5, p: 1, s: 1, t: 2}, what is the expected number of times the pattern 'i*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.82", "dataset": "MATH"}
|
| 75 |
+
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {l: 3, z: 9, f: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.77", "dataset": "MATH"}
|
| 76 |
+
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 6, p: 3, q: 3}, what is the expected number of times the pattern 'q+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
|
| 77 |
+
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 6, k: 6}, 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": "1.64", "dataset": "MATH"}
|
| 78 |
+
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {p: 1, i: 5, h: 2, r: 3, x: 1}, what is the expected number of times the pattern 'ir+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.53", "dataset": "MATH"}
|
| 79 |
+
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 4, u: 3, r: 2, x: 3}, what is the expected number of times the pattern 'rx+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.21", "dataset": "MATH"}
|
| 80 |
+
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 8, r: 5}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.28", "dataset": "MATH"}
|
| 81 |
+
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 5, p: 6}, what is the expected number of times the pattern 'x*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.29", "dataset": "MATH"}
|
| 82 |
+
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 6, b: 1, u: 4}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.73", "dataset": "MATH"}
|
| 83 |
+
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {i: 10, r: 3} to form a word, what is the expected number of matches of the pattern 'ir*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.73", "dataset": "MATH"}
|
| 84 |
+
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 3, w: 6, l: 4}, 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": "0.55", "dataset": "MATH"}
|
| 85 |
+
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {s: 3, m: 3, k: 3, t: 3}. What is the expected number of occurrences of the pattern 't+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
|
| 86 |
+
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {q: 1, s: 1, o: 3, p: 3, c: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.22", "dataset": "MATH"}
|
| 87 |
+
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {h: 6, n: 5} to form a word, what is the expected number of matches of the pattern 'n.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.73", "dataset": "MATH"}
|
| 88 |
+
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {d: 6, o: 5} 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": "1.09", "dataset": "MATH"}
|
| 89 |
+
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, o: 3, q: 3, r: 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": "0.4", "dataset": "MATH"}
|
| 90 |
+
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 7, r: 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": "3.62", "dataset": "MATH"}
|
| 91 |
+
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 6, k: 4}, what is the expected number of times the pattern 'pk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.03", "dataset": "MATH"}
|
| 92 |
+
{"messages": [{"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 4, c: 6}, what is the expected number of times the pattern 'kc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
|
| 93 |
+
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {i: 3, f: 2, w: 10} 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": "0.29", "dataset": "MATH"}
|
| 94 |
+
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {x: 5, z: 5}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.33", "dataset": "MATH"}
|
| 95 |
+
{"messages": [{"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 4, k: 2, l: 3, t: 4}, what is the expected number of times the pattern 'rt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.37", "dataset": "MATH"}
|
| 96 |
+
{"messages": [{"content": "Form a word by randomly choosing 4 letters from the multiset {c: 8, a: 5}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.77", "dataset": "MATH"}
|
| 97 |
+
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {m: 3, t: 4, v: 1, c: 3, b: 4} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.57", "dataset": "MATH"}
|
| 98 |
+
{"messages": [{"content": "When randomly selecting 5 letters from the multiset {y: 4, u: 4, j: 4} to form a word, what is the expected number of matches of the pattern 'y*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.28", "dataset": "MATH"}
|
| 99 |
+
{"messages": [{"content": "Form a word by randomly choosing 5 letters from the multiset {w: 3, f: 3, y: 3, s: 2, r: 1}. What is the expected number of occurrences of the pattern 'y+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.32", "dataset": "MATH"}
|
| 100 |
+
{"messages": [{"content": "When randomly selecting 4 letters from the multiset {j: 6, c: 5} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.64", "dataset": "MATH"}
|