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_0400 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, a: 4}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0401 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {a: 1, g: 3, e: 4}. What is the expected number of occurrences of the pattern 'e.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.29 | math |
combinatory_pattern_matching_train_0402 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 5, k: 2}, what is the expected number of times the pattern 'c+k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.24 | math |
combinatory_pattern_matching_train_0403 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, k: 1, q: 2, i: 1}, what is the expected number of times the pattern 'i*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.77 | math |
combinatory_pattern_matching_train_0404 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, l: 1, f: 1, h: 1}, what is the expected number of times the pattern 'h*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.57 | math |
combinatory_pattern_matching_train_0405 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {l: 1, j: 1, h: 4, e: 1} to form a word, what is the expected number of matches of the pattern 'j*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.64 | math |
combinatory_pattern_matching_train_0406 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, i: 1, d: 2, o: 1}, what is the expected number of times the pattern 'd+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.3 | math |
combinatory_pattern_matching_train_0407 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {j: 1, e: 3, b: 1, z: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0408 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {s: 1, c: 2, y: 2, m: 1, q: 1} to form a word, what is the expected number of matches of the pattern 's+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.05 | math |
combinatory_pattern_matching_train_0409 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {p: 1, x: 1, r: 1, f: 3, h: 1} to form a word, what is the expected number of matches of the pattern 'p*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.64 | math |
combinatory_pattern_matching_train_0410 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, e: 3, x: 2, r: 2}. What is the expected number of occurrences of the pattern 'x+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.15 | math |
combinatory_pattern_matching_train_0411 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {h: 1, v: 2, i: 1, r: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'y*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.57 | math |
combinatory_pattern_matching_train_0412 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {h: 1, s: 2, p: 1, z: 1, j: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.4 | math |
combinatory_pattern_matching_train_0413 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, u: 3}, what is the expected number of times the pattern 'ud+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.75 | math |
combinatory_pattern_matching_train_0414 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 3, p: 4}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.86 | math |
combinatory_pattern_matching_train_0415 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 2, l: 1, x: 2, k: 1, b: 2}. What is the expected number of occurrences of the pattern 'x*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.62 | math |
combinatory_pattern_matching_train_0416 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 3, b: 2, i: 1, y: 2}, what is the expected number of times the pattern 'yc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.4 | math |
combinatory_pattern_matching_train_0417 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, q: 2, z: 1, k: 2}. What is the expected number of occurrences of the pattern 'zk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.45 | math |
combinatory_pattern_matching_train_0418 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 2, p: 2, z: 1, q: 1}, what is the expected number of times the pattern 'z.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0419 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {u: 1, i: 2, x: 1, n: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'm*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.77 | math |
combinatory_pattern_matching_train_0420 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, i: 2, p: 4}. What is the expected number of occurrences of the pattern 'iu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.9 | math |
combinatory_pattern_matching_train_0421 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {g: 2, i: 4}. What is the expected number of occurrences of the pattern 'gi*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.67 | math |
combinatory_pattern_matching_train_0422 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 1, x: 1, e: 3, o: 2}. What is the expected number of occurrences of the pattern 'rx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.64 | math |
combinatory_pattern_matching_train_0423 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {a: 1, t: 1, u: 1, w: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0424 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 2, g: 5, n: 1}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.14 | math |
combinatory_pattern_matching_train_0425 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, y: 4}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.43 | math |
combinatory_pattern_matching_train_0426 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, h: 1, w: 2, g: 1, a: 1}. What is the expected number of occurrences of the pattern 'g+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.13 | math |
combinatory_pattern_matching_train_0427 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, o: 2, d: 2, z: 2}, what is the expected number of times the pattern 'z*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.9 | math |
combinatory_pattern_matching_train_0428 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, a: 2, q: 3}. What is the expected number of occurrences of the pattern 'qx*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.5 | math |
combinatory_pattern_matching_train_0429 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {b: 2, f: 2, e: 1, d: 1}. What is the expected number of occurrences of the pattern 'e+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0430 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, u: 1, n: 2}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0431 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, j: 2, r: 2, v: 1}, what is the expected number of times the pattern 'jv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.13 | math |
combinatory_pattern_matching_train_0432 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 2, s: 2, h: 2, m: 1}, what is the expected number of times the pattern 's+h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.32 | math |
combinatory_pattern_matching_train_0433 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, u: 2, p: 1, f: 1, c: 3}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.32 | math |
combinatory_pattern_matching_train_0434 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 2, s: 3, r: 3}, what is the expected number of times the pattern 'rs*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.1 | math |
combinatory_pattern_matching_train_0435 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, k: 1, j: 1, l: 1, h: 1}, what is the expected number of times the pattern 'j.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0436 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 1, n: 1, m: 1, x: 3}. What is the expected number of occurrences of the pattern 'nx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.42 | math |
combinatory_pattern_matching_train_0437 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 1, k: 1, u: 1, j: 1, n: 2}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0438 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 5, y: 3}, what is the expected number of times the pattern 'y+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.62 | math |
combinatory_pattern_matching_train_0439 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {n: 1, l: 3, o: 1, z: 3} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0440 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 1, a: 5}, what is the expected number of times the pattern 'a.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.0 | math |
combinatory_pattern_matching_train_0441 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 3, e: 1, z: 4}, what is the expected number of times the pattern 'ez+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.3 | math |
combinatory_pattern_matching_train_0442 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {m: 2, u: 3, s: 1} to form a word, what is the expected number of matches of the pattern 'u+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.25 | math |
combinatory_pattern_matching_train_0443 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {g: 3, l: 1, d: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0444 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {s: 4, z: 1, y: 3} to form a word, what is the expected number of matches of the pattern 'yz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.11 | math |
combinatory_pattern_matching_train_0445 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 1, m: 1, j: 1, x: 3, o: 1}, what is the expected number of times the pattern 't.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.14 | math |
combinatory_pattern_matching_train_0446 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {s: 2, q: 1, b: 3, r: 1, c: 1} to form a word, what is the expected number of matches of the pattern 's.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.21 | math |
combinatory_pattern_matching_train_0447 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 1, h: 3, b: 1, o: 1, j: 2}. What is the expected number of occurrences of the pattern 'lb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.55 | math |
combinatory_pattern_matching_train_0448 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 1, g: 2, e: 2, k: 1, f: 2}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.21 | math |
combinatory_pattern_matching_train_0449 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 5, m: 3}, what is the expected number of times the pattern 'mr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.84 | math |
combinatory_pattern_matching_train_0450 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 1, a: 1, y: 2, p: 1, r: 3}, what is the expected number of times the pattern 't.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.21 | math |
combinatory_pattern_matching_train_0451 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {h: 2, s: 2, w: 1, o: 1}. What is the expected number of occurrences of the pattern 'ow+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0452 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {e: 3, p: 3}. What is the expected number of occurrences of the pattern 'ep+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.25 | math |
combinatory_pattern_matching_train_0453 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, y: 1, z: 2, i: 1, c: 1}, what is the expected number of times the pattern 'z*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.65 | math |
combinatory_pattern_matching_train_0454 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 5, h: 3}, what is the expected number of times the pattern 'h+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.62 | math |
combinatory_pattern_matching_train_0455 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 3, g: 2, k: 3}, what is the expected number of times the pattern 'k.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.48 | math |
combinatory_pattern_matching_train_0456 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, d: 1, t: 3, l: 1}, what is the expected number of times the pattern 'dl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.07 | math |
combinatory_pattern_matching_train_0457 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {s: 1, e: 3, k: 2}. What is the expected number of occurrences of the pattern 'se*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.08 | math |
combinatory_pattern_matching_train_0458 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {b: 1, k: 3, m: 2, q: 2}. What is the expected number of occurrences of the pattern 'kk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.36 | math |
combinatory_pattern_matching_train_0459 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {t: 5, r: 3}. What is the expected number of occurrences of the pattern 't+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.27 | math |
combinatory_pattern_matching_train_0460 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, b: 3}, what is the expected number of times the pattern 'o+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.45 | math |
combinatory_pattern_matching_train_0461 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, n: 1, v: 2}, what is the expected number of times the pattern 'mv+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.45 | math |
combinatory_pattern_matching_train_0462 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 1, t: 3, a: 2}, what is the expected number of times the pattern 'wa+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.23 | math |
combinatory_pattern_matching_train_0463 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {y: 4, z: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.32 | math |
combinatory_pattern_matching_train_0464 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {r: 1, e: 1, q: 1, t: 1, p: 3} to form a word, what is the expected number of matches of the pattern 'p.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.21 | math |
combinatory_pattern_matching_train_0465 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {q: 2, w: 2, i: 1, g: 3} to form a word, what is the expected number of matches of the pattern 'q*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.24 | math |
combinatory_pattern_matching_train_0466 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 2, n: 5}. What is the expected number of occurrences of the pattern 'r.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.43 | math |
combinatory_pattern_matching_train_0467 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, k: 1, a: 2, y: 1, l: 1}, what is the expected number of times the pattern 'ny*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.57 | math |
combinatory_pattern_matching_train_0468 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {i: 2, x: 2, m: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'i.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.57 | math |
combinatory_pattern_matching_train_0469 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {s: 2, k: 1, q: 1, o: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'r+s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.13 | math |
combinatory_pattern_matching_train_0470 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, f: 1, b: 6}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0471 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, p: 1, m: 3}, what is the expected number of times the pattern 'p+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0472 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {k: 2, s: 2, t: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'ts*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.47 | math |
combinatory_pattern_matching_train_0473 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, j: 2, g: 2}, what is the expected number of times the pattern 'j.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.43 | math |
combinatory_pattern_matching_train_0474 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, f: 1, z: 1, b: 2}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0475 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, o: 2, b: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.86 | math |
combinatory_pattern_matching_train_0476 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {b: 4, r: 3}. What is the expected number of occurrences of the pattern 'rb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.74 | math |
combinatory_pattern_matching_train_0477 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, o: 1, d: 4}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0478 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 1, f: 2, q: 2, w: 2, h: 1}, what is the expected number of times the pattern 'hq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.62 | math |
combinatory_pattern_matching_train_0479 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {l: 1, w: 3, u: 1, q: 3} to form a word, what is the expected number of matches of the pattern 'lq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0480 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {y: 4, o: 1, x: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'ya+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.14 | math |
combinatory_pattern_matching_train_0481 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, u: 2, j: 2}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.14 | math |
combinatory_pattern_matching_train_0482 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, b: 2, w: 1, r: 4}, what is the expected number of times the pattern 'r.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.43 | math |
combinatory_pattern_matching_train_0483 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, w: 4}. What is the expected number of occurrences of the pattern 'wb*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.4 | math |
combinatory_pattern_matching_train_0484 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 2, h: 1, z: 3, e: 1, r: 1}, what is the expected number of times the pattern 'e.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0485 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, t: 1, b: 1, s: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.6 | math |
combinatory_pattern_matching_train_0486 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 2, z: 2, a: 2, f: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.21 | math |
combinatory_pattern_matching_train_0487 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {b: 2, t: 3, m: 1, z: 1}, what is the expected number of times the pattern 'z*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.64 | math |
combinatory_pattern_matching_train_0488 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {d: 3, q: 1, c: 3} to form a word, what is the expected number of matches of the pattern 'q*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.93 | math |
combinatory_pattern_matching_train_0489 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, a: 2, f: 1, n: 3}. What is the expected number of occurrences of the pattern 'g.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0490 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 3, i: 3}, what is the expected number of times the pattern 'g.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.9 | math |
combinatory_pattern_matching_train_0491 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, a: 1, h: 2, d: 2}, what is the expected number of times the pattern 'd.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.29 | math |
combinatory_pattern_matching_train_0492 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, g: 2, p: 1, b: 3}. What is the expected number of occurrences of the pattern 'b.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.43 | math |
combinatory_pattern_matching_train_0493 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 1, r: 2, j: 2, d: 1, o: 2}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0494 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, y: 5}, what is the expected number of times the pattern 'y*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.84 | math |
combinatory_pattern_matching_train_0495 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 1, j: 1, f: 1, y: 1, d: 2}, what is the expected number of times the pattern 'd*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.9 | math |
combinatory_pattern_matching_train_0496 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {x: 3, p: 1, h: 1, k: 1, y: 2} to form a word, what is the expected number of matches of the pattern 'y.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.11 | math |
combinatory_pattern_matching_train_0497 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {q: 3, c: 3, i: 2}. What is the expected number of occurrences of the pattern 'i.*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.11 | math |
combinatory_pattern_matching_train_0498 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 5, k: 2, e: 1}. What is the expected number of occurrences of the pattern 'ek+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.08 | math |
combinatory_pattern_matching_train_0499 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 1, j: 2, g: 1, f: 1, i: 2}, what is the expected number of times the pattern 'f+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.14 | math |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.