messages listlengths 1 1 | ground_truth stringclasses 13
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 3, u: 1}, what is the expected number of times the pattern 'uq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {z: 2, o: 2}, what is the expected number of times the pattern 'z+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {y: 2, s: 1, z: 1}. What is the expected number of occurrences of the pattern 'y+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {b: 3, q: 1}. What is the expected number of occurrences of the pattern 'q.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 1, i: 1, t: 1, s: 1}, what is the expected number of times the pattern 'ts+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {l: 1, a: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'g.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {f: 1, l: 1, y: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'yl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {i: 1, j: 1, v: 1, c: 1}, what is the expected number of times the pattern 'j.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {b: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {o: 2, z: 1, f: 1}. What is the expected number of occurrences of the pattern 'z.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {c: 2, r: 2} to form a word, what is the expected number of matches of the pattern 'r.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {q: 1, y: 1, w: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'wy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {l: 1, p: 2, t: 1}, what is the expected number of times the pattern 'p+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 1, n: 1, q: 1, r: 1}, what is the expected number of times the pattern 'x+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {t: 2, d: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {o: 1, g: 1, b: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'oo+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 1, d: 1, k: 1, y: 1}, what is the expected number of times the pattern 'dy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {b: 1, z: 1, r: 1, h: 1}. What is the expected number of occurrences of the pattern 'rr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 1, y: 1, q: 2}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {m: 1, t: 1, d: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'dt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 1, n: 1, e: 1, k: 1}, what is the expected number of times the pattern 'k*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {h: 1, y: 3} to form a word, what is the expected number of matches of the pattern 'hy+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {w: 1, c: 1, i: 1, t: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {y: 1, r: 1, f: 1, s: 1} to form a word, what is the expected number of matches of the pattern 's.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {r: 2, a: 2}. What is the expected number of occurrences of the pattern 'r*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {p: 3, i: 1}. What is the expected number of occurrences of the pattern 'i.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 1, o: 1, v: 1, h: 1}, what is the expected number of times the pattern 'v+o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {x: 1, k: 1, f: 1, q: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {n: 2, a: 2} to form a word, what is the expected number of matches of the pattern 'an+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {i: 1, k: 1, g: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'i*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {n: 1, u: 1, d: 1, k: 1} to form a word, what is the expected number of matches of the pattern 'k.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 1, n: 1, o: 2}, what is the expected number of times the pattern 'n*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {m: 1, u: 1, f: 2}. What is the expected number of occurrences of the pattern 'm*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {u: 1, i: 3}. What is the expected number of occurrences of the pattern 'i.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {q: 2, r: 2} to form a word, what is the expected number of matches of the pattern 'rq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {u: 1, v: 2, j: 1}. What is the expected number of occurrences of the pattern 'v.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {k: 2, z: 1, q: 1}. What is the expected number of occurrences of the pattern 'z.*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 2, f: 2}, what is the expected number of times the pattern 'u+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {j: 1, c: 1, w: 1, g: 1}, what is the expected number of times the pattern 'w.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {b: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'nn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {a: 2, m: 1, h: 1}. What is the expected number of occurrences of the pattern 'ma+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {s: 1, h: 1, a: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'sa+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {y: 1, n: 1, m: 1, i: 1}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {p: 2, g: 2}. What is the expected number of occurrences of the pattern 'pg+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {y: 1, p: 3} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {j: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 1, s: 1, l: 2}, what is the expected number of times the pattern 'u*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {m: 1, y: 1, i: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {l: 1, x: 1, q: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'tx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {q: 1, y: 1, a: 2} to form a word, what is the expected number of matches of the pattern 'q.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {i: 1, x: 3} to form a word, what is the expected number of matches of the pattern 'i*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.75 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 1, m: 3}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {z: 1, o: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'v*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.67 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {p: 2, g: 2}. What is the expected number of occurrences of the pattern 'g.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {v: 1, w: 3}. What is the expected number of occurrences of the pattern 'wv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {s: 2, i: 2}. What is the expected number of occurrences of the pattern 'si+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {l: 1, p: 1, a: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'pl+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {a: 1, v: 3}, what is the expected number of times the pattern 'v*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.75 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 1, e: 2, w: 1}, what is the expected number of times the pattern 'e+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {q: 1, n: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {x: 2, f: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'x.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {k: 1, i: 1, n: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'i.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {p: 2, x: 2} to form a word, what is the expected number of matches of the pattern 'px*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {d: 2, v: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 1, 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"
}
] | 0.5 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {r: 1, h: 1, m: 1, y: 1}. What is the expected number of occurrences of the pattern 'r.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 1, c: 1, m: 1, o: 1}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {c: 2, i: 1, m: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 1, s: 1, o: 1, t: 1}, what is the expected number of times the pattern 'os*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {p: 1, k: 1, d: 1, t: 1}. What is the expected number of occurrences of the pattern 'pk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {a: 2, c: 2}, what is the expected number of times the pattern 'a+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 2, g: 2}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {k: 1, r: 1, b: 1, n: 1}. What is the expected number of occurrences of the pattern 'n+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {e: 2, t: 1, v: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 1, t: 1, x: 1, u: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {p: 1, y: 1, q: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {x: 1, l: 1, d: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'dp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {b: 1, j: 1, k: 1, q: 1}. What is the expected number of occurrences of the pattern 'q+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {a: 1, l: 2, s: 1}, what is the expected number of times the pattern 'l*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.67 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {s: 1, f: 2, h: 1}. What is the expected number of occurrences of the pattern 'sh*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {o: 1, v: 1, a: 1, n: 1}. What is the expected number of occurrences of the pattern 'a+v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 1, c: 1, n: 1, t: 1}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {r: 1, t: 1, g: 2}. What is the expected number of occurrences of the pattern 'gt+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {b: 2, j: 2}, what is the expected number of times the pattern 'jj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {f: 1, w: 2, p: 1}. What is the expected number of occurrences of the pattern 'p+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {e: 2, t: 2} to form a word, what is the expected number of matches of the pattern 'e.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 1, l: 3}, what is the expected number of times the pattern 'w.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 2, x: 1, r: 1}, what is the expected number of times the pattern 'x.*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {z: 1, c: 1, i: 1, o: 1}, what is the expected number of times the pattern 'iz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {a: 1, u: 1, e: 1, o: 1}, what is the expected number of times the pattern 'u+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 2, b: 2}, what is the expected number of times the pattern 'p+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {d: 1, h: 1, m: 1, w: 1}. What is the expected number of occurrences of the pattern 'hd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 1, c: 1, q: 1, u: 1}, what is the expected number of times the pattern 'e*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {j: 1, w: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'jw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {i: 1, o: 1, y: 1, n: 1}. What is the expected number of occurrences of the pattern 'o.*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {t: 1, p: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 1, z: 1, i: 1, p: 1}, what is the expected number of times the pattern 'hp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {k: 1, i: 1, q: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'wi+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {m: 2, d: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 2, p: 1, g: 1}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.