id stringlengths 39 39 | setting_key stringclasses 1
value | setting_name stringclasses 0
values | messages listlengths 1 1 | ground_truth stringclasses 126
values | dataset stringclasses 1
value |
|---|---|---|---|---|---|
combinatory_pattern_matching_train_0500 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 3, k: 1, x: 1, d: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.86 | math |
combinatory_pattern_matching_train_0501 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, p: 3, w: 1, o: 1, x: 1}. What is the expected number of occurrences of the pattern 'n+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.14 | math |
combinatory_pattern_matching_train_0502 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {q: 2, r: 1, g: 1, u: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'nu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.14 | math |
combinatory_pattern_matching_train_0503 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 4, y: 2}, what is the expected number of times the pattern 'o*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.67 | math |
combinatory_pattern_matching_train_0504 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {k: 6, m: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'q*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.55 | math |
combinatory_pattern_matching_train_0505 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, g: 1, v: 1, q: 1, k: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0506 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {m: 2, e: 2, q: 4}. What is the expected number of occurrences of the pattern 'eq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.6 | math |
combinatory_pattern_matching_train_0507 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, c: 4, a: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.2 | math |
combinatory_pattern_matching_train_0508 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {j: 1, l: 1, q: 2, b: 1, z: 3} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0509 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 3, a: 2, m: 1, e: 1}, what is the expected number of times the pattern 'a.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.29 | math |
combinatory_pattern_matching_train_0510 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {a: 1, j: 2, m: 1, z: 3} to form a word, what is the expected number of matches of the pattern 'j*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.2 | math |
combinatory_pattern_matching_train_0511 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {k: 4, v: 2} to form a word, what is the expected number of matches of the pattern 'k+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.33 | math |
combinatory_pattern_matching_train_0512 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 2, x: 2, z: 2, g: 2}, what is the expected number of times the pattern 'z+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.24 | math |
combinatory_pattern_matching_train_0513 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {u: 4, n: 3} to form a word, what is the expected number of matches of the pattern 'u+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.29 | math |
combinatory_pattern_matching_train_0514 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, y: 1, l: 3, m: 1, i: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.32 | math |
combinatory_pattern_matching_train_0515 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, d: 2, m: 1, y: 2, h: 1}, what is the expected number of times the pattern 'n*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.95 | math |
combinatory_pattern_matching_train_0516 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, m: 1, n: 1, i: 2, p: 2}, what is the expected number of times the pattern 'np*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.62 | math |
combinatory_pattern_matching_train_0517 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 2, m: 1, j: 4}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.86 | math |
combinatory_pattern_matching_train_0518 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {o: 1, f: 3, d: 3, l: 1} to form a word, what is the expected number of matches of the pattern 'o+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.16 | math |
combinatory_pattern_matching_train_0519 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {m: 1, n: 2, o: 1, g: 1, h: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0520 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {h: 1, q: 2, v: 1, d: 2, z: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.21 | math |
combinatory_pattern_matching_train_0521 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 1, w: 1, l: 2, b: 2}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0522 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 4, m: 3, t: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.64 | math |
combinatory_pattern_matching_train_0523 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {t: 4, l: 3}. What is the expected number of occurrences of the pattern 'l.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.71 | math |
combinatory_pattern_matching_train_0524 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {w: 4, e: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'w+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.86 | math |
combinatory_pattern_matching_train_0525 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {n: 1, o: 2, y: 1, v: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'o*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.53 | math |
combinatory_pattern_matching_train_0526 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {u: 5, q: 2}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.43 | math |
combinatory_pattern_matching_train_0527 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, j: 1, f: 1, a: 2, v: 1}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0528 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {u: 4, n: 3}. What is the expected number of occurrences of the pattern 'u.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.71 | math |
combinatory_pattern_matching_train_0529 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, x: 1, w: 1, q: 1, l: 1}. What is the expected number of occurrences of the pattern 'x.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0530 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {b: 2, x: 5, o: 1} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.14 | math |
combinatory_pattern_matching_train_0531 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {n: 3, m: 4} to form a word, what is the expected number of matches of the pattern 'n*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.4 | math |
combinatory_pattern_matching_train_0532 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {u: 1, b: 1, i: 1, z: 1, k: 2} to form a word, what is the expected number of matches of the pattern 'z*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.77 | math |
combinatory_pattern_matching_train_0533 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, s: 6}, what is the expected number of times the pattern 'u+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.46 | math |
combinatory_pattern_matching_train_0534 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {o: 1, u: 1, c: 1, v: 2, s: 1}. What is the expected number of occurrences of the pattern 'c.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.4 | math |
combinatory_pattern_matching_train_0535 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {g: 1, j: 2, n: 1, x: 1, a: 3} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0536 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {x: 4, y: 3} to form a word, what is the expected number of matches of the pattern 'y+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.69 | math |
combinatory_pattern_matching_train_0537 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 4, g: 3}, what is the expected number of times the pattern 'x+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.74 | math |
combinatory_pattern_matching_train_0538 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 5, k: 2}. What is the expected number of occurrences of the pattern 'l*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.38 | math |
combinatory_pattern_matching_train_0539 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {e: 1, n: 1, c: 1, h: 2, w: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0540 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {o: 5, p: 2}. What is the expected number of occurrences of the pattern 'po+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.67 | math |
combinatory_pattern_matching_train_0541 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {o: 3, c: 3, w: 1} to form a word, what is the expected number of matches of the pattern 'w.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.21 | math |
combinatory_pattern_matching_train_0542 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, q: 1, v: 2, e: 3}. What is the expected number of occurrences of the pattern 'yv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0543 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, r: 2, p: 2}, what is the expected number of times the pattern 'p+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.3 | math |
combinatory_pattern_matching_train_0544 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, y: 1, f: 5}. What is the expected number of occurrences of the pattern 'fc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.26 | math |
combinatory_pattern_matching_train_0545 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {c: 3, e: 4, x: 1} to form a word, what is the expected number of matches of the pattern 'x+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.16 | math |
combinatory_pattern_matching_train_0546 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, y: 2, t: 3}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.14 | math |
combinatory_pattern_matching_train_0547 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 2, p: 1, e: 3}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.2 | math |
combinatory_pattern_matching_train_0548 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {x: 3, g: 4}. What is the expected number of occurrences of the pattern 'g+x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.29 | math |
combinatory_pattern_matching_train_0549 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 3, p: 4}, what is the expected number of times the pattern 'p.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.71 | math |
combinatory_pattern_matching_train_0550 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, f: 3, c: 1, j: 2}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0551 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, i: 2, a: 1, w: 3}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0552 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 4, l: 1, u: 1}, what is the expected number of times the pattern 'ug+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.37 | math |
combinatory_pattern_matching_train_0553 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, n: 4, l: 1}. What is the expected number of occurrences of the pattern 'll+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0554 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 5, e: 3}, what is the expected number of times the pattern 'ey+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.71 | math |
combinatory_pattern_matching_train_0555 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, o: 1, z: 3, n: 3}, what is the expected number of times the pattern 'o*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.41 | math |
combinatory_pattern_matching_train_0556 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 3, e: 3}, what is the expected number of times the pattern 'te+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.75 | math |
combinatory_pattern_matching_train_0557 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {s: 2, p: 2, j: 3}. What is the expected number of occurrences of the pattern 's+p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.32 | math |
combinatory_pattern_matching_train_0558 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, x: 1, j: 1, p: 1, k: 2}. What is the expected number of occurrences of the pattern 'x+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0559 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {t: 1, r: 1, v: 1, h: 2, x: 1}. What is the expected number of occurrences of the pattern 'rx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0560 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 3, x: 3, y: 2}. What is the expected number of occurrences of the pattern 'x+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.6 | math |
combinatory_pattern_matching_train_0561 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, t: 4}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.2 | math |
combinatory_pattern_matching_train_0562 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {h: 2, q: 3, k: 1}. What is the expected number of occurrences of the pattern 'k.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.6 | math |
combinatory_pattern_matching_train_0563 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, y: 5}, what is the expected number of times the pattern 'y+u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.71 | math |
combinatory_pattern_matching_train_0564 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, u: 1, s: 2, l: 2, h: 2}. What is the expected number of occurrences of the pattern 'hl+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.15 | math |
combinatory_pattern_matching_train_0565 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 3, j: 1, v: 2, c: 2}, what is the expected number of times the pattern 'cv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.24 | math |
combinatory_pattern_matching_train_0566 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, m: 2, v: 1, e: 2, g: 2}. What is the expected number of occurrences of the pattern 'vt*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.41 | math |
combinatory_pattern_matching_train_0567 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {g: 2, l: 2, i: 3, a: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.21 | math |
combinatory_pattern_matching_train_0568 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, h: 2, a: 1, x: 1}, what is the expected number of times the pattern 'h+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.13 | math |
combinatory_pattern_matching_train_0569 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {a: 2, l: 3, o: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'z*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.24 | math |
combinatory_pattern_matching_train_0570 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {l: 3, m: 3}. What is the expected number of occurrences of the pattern 'ml+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.75 | math |
combinatory_pattern_matching_train_0571 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {i: 1, g: 2, t: 2, n: 3}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0572 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, i: 1, n: 5}, what is the expected number of times the pattern 'n.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.36 | math |
combinatory_pattern_matching_train_0573 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {v: 2, s: 3, h: 2, p: 1} to form a word, what is the expected number of matches of the pattern 's.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.32 | math |
combinatory_pattern_matching_train_0574 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, i: 2, z: 1, u: 2, h: 1}, what is the expected number of times the pattern 'm.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.07 | math |
combinatory_pattern_matching_train_0575 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 1, j: 2, a: 3, h: 1}, what is the expected number of times the pattern 'h+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.07 | math |
combinatory_pattern_matching_train_0576 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, m: 2, i: 2, n: 1}. What is the expected number of occurrences of the pattern 'n.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0577 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {m: 1, t: 1, u: 1, d: 2, g: 2} to form a word, what is the expected number of matches of the pattern 'u.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.07 | math |
combinatory_pattern_matching_train_0578 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {f: 1, x: 1, i: 1, k: 1, n: 4} to form a word, what is the expected number of matches of the pattern 'x*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.41 | math |
combinatory_pattern_matching_train_0579 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {q: 1, w: 2, r: 1, i: 1, e: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0580 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, w: 1, t: 2, m: 2, z: 1}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0581 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 1, d: 2, o: 2, m: 1, z: 2}, what is the expected number of times the pattern 'zo*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.24 | math |
combinatory_pattern_matching_train_0582 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, u: 1, e: 3}. What is the expected number of occurrences of the pattern 'e.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.21 | math |
combinatory_pattern_matching_train_0583 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, x: 2, i: 1, s: 2}, what is the expected number of times the pattern 's.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.29 | math |
combinatory_pattern_matching_train_0584 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {j: 1, c: 3, w: 2, r: 2} to form a word, what is the expected number of matches of the pattern 'c+j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0585 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, j: 2, y: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.14 | math |
combinatory_pattern_matching_train_0586 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 4, p: 4}, what is the expected number of times the pattern 'pv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.2 | math |
combinatory_pattern_matching_train_0587 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 5, a: 1, g: 1}, what is the expected number of times the pattern 'af*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.19 | math |
combinatory_pattern_matching_train_0588 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {d: 1, u: 2, w: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'wd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0589 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, n: 4, r: 1}. What is the expected number of occurrences of the pattern 'f.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.4 | math |
combinatory_pattern_matching_train_0590 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {j: 1, f: 3, l: 4} to form a word, what is the expected number of matches of the pattern 'l.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.21 | math |
combinatory_pattern_matching_train_0591 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {n: 1, v: 3, c: 1, t: 2} to form a word, what is the expected number of matches of the pattern 'n+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.21 | math |
combinatory_pattern_matching_train_0592 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 1, w: 2, k: 2, p: 2}, what is the expected number of times the pattern 'm+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.14 | math |
combinatory_pattern_matching_train_0593 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, t: 2, v: 1, b: 1, y: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0594 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, v: 2, k: 2}. What is the expected number of occurrences of the pattern 'z+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.3 | math |
combinatory_pattern_matching_train_0595 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 1, m: 3, v: 3}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.86 | math |
combinatory_pattern_matching_train_0596 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {q: 3, i: 4, b: 1} to form a word, what is the expected number of matches of the pattern 'ib*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.64 | math |
combinatory_pattern_matching_train_0597 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {b: 1, z: 2, j: 1, e: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'e.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0598 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 2, j: 1, d: 3, r: 2}. What is the expected number of occurrences of the pattern 'd+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.4 | math |
combinatory_pattern_matching_train_0599 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, x: 1, t: 1, v: 3}, what is the expected number of times the pattern 'k*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.7 | math |
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