messages listlengths 1 1 | ground_truth stringclasses 38
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, e: 1, m: 2}. What is the expected number of occurrences of the pattern 'e+d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 2, s: 2, y: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'p+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.15 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {b: 1, i: 3, p: 2} to form a word, what is the expected number of matches of the pattern 'ip+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.45 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 3, j: 1, v: 2}, 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}",
"role": "user"
}
] | 0.65 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {u: 2, k: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, z: 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}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, c: 1, r: 2, h: 1}, what is the expected number of times the pattern 'hr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.65 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, g: 2, v: 2}, what is the expected number of times the pattern 'v.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, l: 3, p: 1}, what is the expected number of times the pattern 'ps+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.15 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {t: 1, h: 1, k: 1, v: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'z.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {w: 3, a: 3}. What is the expected number of occurrences of the pattern 'w.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.9 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, o: 1, x: 1, d: 1, r: 1}. What is the expected number of occurrences of the pattern 'r.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {v: 1, g: 1, n: 2, x: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'gx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, d: 2, v: 2, q: 1}. What is the expected number of occurrences of the pattern 'vq+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, u: 2, g: 3}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {q: 2, d: 4} to form a word, what is the expected number of matches of the pattern 'qd+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.73 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {a: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'u*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.25 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {a: 1, o: 1, d: 1, n: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, o: 1, d: 2, i: 2}. What is the expected number of occurrences of the pattern 'i+g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.15 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {s: 2, a: 1, t: 1, k: 1, h: 1}. What is the expected number of occurrences of the pattern 'a+k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {z: 2, w: 1, p: 3} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {c: 1, g: 1, k: 2, p: 2} to form a word, what is the expected number of matches of the pattern 'p*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.3 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {u: 3, q: 3}. What is the expected number of occurrences of the pattern 'q.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.9 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, w: 3}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, a: 1, d: 1, f: 1, t: 1}, what is the expected number of times the pattern 'wf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {t: 2, z: 1, g: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'hg+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, c: 2, r: 1, w: 1}. What is the expected number of occurrences of the pattern 'rw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.57 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {x: 1, q: 2, r: 1, a: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'a.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {v: 3, k: 1, b: 2} to form a word, what is the expected number of matches of the pattern 'v+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.45 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {d: 3, s: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'd+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {b: 2, m: 1, k: 1, d: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, c: 4}, 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"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {m: 2, l: 4} to form a word, what is the expected number of matches of the pattern 'l+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.73 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, y: 2, o: 2}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {g: 1, t: 2, b: 1, p: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, k: 1, q: 1, b: 1, d: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {k: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'k*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.25 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {d: 1, q: 1, a: 2, o: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, w: 3, k: 2}. What is the expected number of occurrences of the pattern 'yw+' 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 3 letters from the multiset {l: 2, h: 1, w: 3} to form a word, what is the expected number of matches of the pattern 'l*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.65 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {o: 1, l: 5} to form a word, what is the expected number of matches of the pattern 'l*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {m: 1, e: 3, j: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'm.*m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, g: 3, x: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, c: 1, f: 1, d: 1, x: 2}. What is the expected number of occurrences of the pattern 'x.*x' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {h: 2, l: 1, y: 1, u: 1, d: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, w: 1, f: 1, e: 1, x: 1}, what is the expected number of times the pattern 'e+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {l: 2, z: 1, w: 2, f: 1}. What is the expected number of occurrences of the pattern 'lf*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.13 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, a: 1, e: 2, p: 2}. What is the expected number of occurrences of the pattern 'e.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {d: 2, o: 1, s: 3} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, f: 4}, what is the expected number of times the pattern 'm.*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.8 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, e: 2, u: 2}. What is the expected number of occurrences of the pattern 'uw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, c: 1, f: 1, a: 1, z: 1}. What is the expected number of occurrences of the pattern 'z*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.57 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, e: 2, m: 1, i: 2}, what is the expected number of times the pattern 'ie*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.3 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 2, w: 1, a: 1, i: 1, d: 1}, what is the expected number of times the pattern 'ca+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {h: 4, d: 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"
}
] | 1.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {j: 5, a: 1} to form a word, what is the expected number of matches of the pattern 'a.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, a: 1, s: 1, j: 1, g: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, x: 5}, what is the expected number of times the pattern 'o+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {k: 3, n: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, q: 2, o: 2}, what is the expected number of times the pattern 'f.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {x: 2, k: 1, p: 1, n: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'gk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.57 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 3, o: 1, w: 1, b: 1}, what is the expected number of times the pattern 'w+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {s: 1, t: 1, z: 4}. What is the expected number of occurrences of the pattern 't+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.27 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {h: 3, i: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'iv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.65 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {g: 2, l: 2, e: 1, k: 1}. 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}",
"role": "user"
}
] | 1.13 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {g: 1, b: 1, s: 1, x: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'xx+'? 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 3 letters from the multiset {h: 1, g: 1, l: 1, d: 1, f: 2}. What is the expected number of occurrences of the pattern 'd.*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {v: 1, g: 2, e: 1, t: 2}. 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}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {s: 1, j: 1, w: 2, y: 1, k: 1} 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"
}
] | 0.65 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {o: 3, t: 3} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {y: 2, f: 2, s: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'fv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {g: 2, r: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'yr*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.3 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, i: 1, p: 1, c: 2, y: 1}. What is the expected number of occurrences of the pattern 'p+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {b: 3, l: 2, s: 1}. What is the expected number of occurrences of the pattern 'sb*' in each word? Round your answer 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 3 by randomly selecting letters from the multiset {g: 2, z: 4}, 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"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, x: 2, u: 3}, what is the expected number of times the pattern 'v+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, x: 1, r: 2, s: 1, a: 1}, 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 4, m: 2}. What is the expected number of occurrences of the pattern 'r.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, a: 2, x: 1, s: 1, t: 1}. What is the expected number of occurrences of the pattern 'sa+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.15 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {v: 3, q: 3} to form a word, what is the expected number of matches of the pattern 'qv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.25 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 3, q: 3}, what is the expected number of times the pattern 'l*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.25 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 1, y: 1, r: 2, p: 1, i: 1}, what is the expected number of times the pattern 'p+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, x: 3, s: 1}. What is the expected number of occurrences of the pattern 'xv+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.45 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, m: 1, d: 1, a: 1, o: 1}, what is the expected number of times the pattern 'da*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.57 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {l: 1, b: 2, a: 2, h: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {g: 4, r: 2}. What is the expected number of occurrences of the pattern 'gr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.6 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {h: 1, i: 1, f: 1, l: 3} 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 3 letters from the multiset {t: 1, e: 1, x: 4} to form a word, what is the expected number of matches of the pattern 'e+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.27 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, r: 1, s: 1, v: 1, d: 2}. What is the expected number of occurrences of the pattern 'sx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 4, h: 1, c: 1}, what is the expected number of times the pattern 'c.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, d: 4}. 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"
}
] | 3.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, k: 4}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {v: 2, m: 3, t: 1} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, p: 1, k: 1, l: 1, w: 1}, what is the expected number of times the pattern 'wl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {b: 2, d: 4} 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"
}
] | 1.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, i: 2, y: 3}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {k: 3, c: 3} to form a word, what is the expected number of matches of the pattern 'k.*k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {j: 1, p: 3, t: 2} to form a word, what is the expected number of matches of the pattern 'jp*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.75 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, v: 1, d: 3, w: 1}. 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"
}
] | 0.57 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, s: 2, m: 3}, what is the expected number of times the pattern 'm.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.