messages listlengths 1 1 | ground_truth stringclasses 38
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, e: 3, m: 1, j: 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}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {u: 1, c: 2, z: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'u*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.13 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 1, k: 2, s: 1, r: 2}, 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"
}
] | 0.57 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, o: 2, u: 1, x: 1, m: 1}, what is the expected number of times the pattern 'o.*m' 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 {a: 4, t: 2}, what is the expected number of times the pattern 'at+' appears? 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 {q: 1, l: 1, u: 1, c: 2, s: 1} 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": "Form a word by randomly choosing 3 letters from the multiset {a: 3, n: 3}. What is the expected number of occurrences of the pattern 'na+' 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": "Form a word by randomly choosing 3 letters from the multiset {c: 3, u: 3}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, f: 1, n: 2, y: 1, k: 1}. What is the expected number of occurrences of the pattern 'y+n' 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 {x: 1, d: 2, l: 1, b: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {n: 1, v: 1, d: 2, r: 2}. What is the expected number of occurrences of the pattern 'v.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, m: 2, t: 2}, what is the expected number of times the pattern 'm+q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {o: 2, k: 1, y: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'o+t'? Round 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 {y: 4, e: 2}. What is the expected number of occurrences of the pattern 'ey+' in each word? Round your answer 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 {l: 2, t: 4}, what is the expected number of times the pattern 'l*t' appears? Round 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 {c: 4, w: 2} 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"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 4, v: 2}, what is the expected number of times the pattern 'k+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.73 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, s: 1, x: 1, m: 1, a: 1}, what is the expected number of times the pattern 'ax+' appears? Round 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 {x: 2, m: 1, l: 1, d: 1, y: 1}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {o: 3, q: 3} 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"
}
] | 0.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, x: 3}, what is the expected number of times the pattern 'x.*x' appears? 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 {c: 1, u: 2, m: 3}, what is the expected number of times the pattern 'cm*' appears? 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 {s: 1, p: 2, u: 1, a: 1, h: 1}. What is the expected number of occurrences of the pattern 'ha*' 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 {x: 4, j: 2}, what is the expected number of times the pattern 'xj+' appears? 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 {x: 2, v: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'vx+'? Round 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 {g: 2, t: 3, q: 1}. What is the expected number of occurrences of the pattern 'q+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": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 2, x: 1, o: 1, g: 2}, what is the expected number of times the pattern 'x.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {j: 1, l: 2, k: 1, e: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'ke*'? 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 {d: 2, m: 1, e: 1, g: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'gq+'? Round 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 {a: 2, l: 2, m: 1, z: 1}, what is the expected number of times the pattern 'za*' 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 {g: 3, q: 1, a: 1, w: 1} 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 {g: 1, r: 1, t: 1, u: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'g*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.57 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, m: 3, e: 1}. What is the expected number of occurrences of the pattern 'j.*j' 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 {y: 2, a: 4}. What is the expected number of occurrences of the pattern 'ya+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.73 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, t: 3}. What is the expected number of occurrences of the pattern 'k.*t' 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": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, e: 1, j: 1, p: 1, z: 1}, what is the expected number of times the pattern 'p*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.57 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, r: 1, h: 1, s: 2, j: 1}. What is the expected number of occurrences of the pattern 'gh+' 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 {n: 2, q: 4}. What is the expected number of occurrences of the pattern 'q+n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.73 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 1, v: 1, e: 1, w: 2, k: 1}. What is the expected number of occurrences of the pattern 'w.*k' 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 {e: 1, c: 1, h: 1, a: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'e+h'? 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 {d: 4, q: 2} to form a word, what is the expected number of matches of the pattern 'd*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.73 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {k: 4, o: 2}. What is the expected number of occurrences of the pattern 'k.*o' in each word? Round your answer 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 {y: 1, g: 1, q: 1, i: 1, t: 2}. What is the expected number of occurrences of the pattern 'gq*' 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 {j: 3, r: 3}, 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"
}
] | 0.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, m: 4}, what is the expected number of times the pattern 'm*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.73 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {a: 3, j: 1, v: 2}. What is the expected number of occurrences of the pattern 'va+' 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": "Form a word by randomly choosing 3 letters from the multiset {j: 3, v: 3}. What is the expected number of occurrences of the pattern 'j.*j' 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 {m: 2, c: 4} to form a word, what is the expected number of matches of the pattern 'mc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.73 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, d: 2, v: 1, b: 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, d: 2, l: 2}. What is the expected number of occurrences of the pattern 'd*l' in each word? Round your answer 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 {f: 2, p: 1, c: 2, z: 1}, what is the expected number of times the pattern 'c+z' 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 {m: 3, v: 1, l: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'm+v'? 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 {z: 1, h: 2, i: 3} to form a word, what is the expected number of matches of the pattern 'zh+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.15 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, l: 2, t: 2, y: 1}, what is the expected number of times the pattern 'ya+' 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 {y: 4, f: 2}. 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"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {c: 2, d: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'dc*'? 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 {l: 2, r: 4}. What is the expected number of occurrences of the pattern 'r*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.73 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {u: 2, q: 1, a: 1, r: 1, v: 1}. What is the expected number of occurrences of the pattern 'av+' 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 {d: 4, y: 2} to form a word, what is the expected number of matches of the pattern 'yd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.73 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 1, w: 5}, 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"
}
] | 0.33 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {g: 1, i: 2, f: 1, p: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'ff+'? 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 {o: 1, y: 1, q: 2, x: 2} 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": "Form a word by randomly choosing 3 letters from the multiset {x: 3, p: 2, d: 1}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {u: 4, v: 2}. What is the expected number of occurrences of the pattern 'vu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.73 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, h: 2, p: 1}, what is the expected number of times the pattern 'px+' appears? 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 3 letters from the multiset {d: 1, g: 1, q: 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {f: 3, m: 3}. 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"
}
] | 0.6 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, j: 1, l: 2, s: 1, v: 1}. What is the expected number of occurrences of the pattern 'lt*' 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": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, k: 3}, what is the expected number of times the pattern 'k.*f' appears? Round 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 {w: 1, k: 5}. 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 3 letters from the multiset {x: 2, w: 4} to form a word, what is the expected number of matches of the pattern 'w+x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.73 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 2, p: 1, m: 1, x: 1, q: 1}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, z: 2, b: 2}. What is the expected number of occurrences of the pattern 'jj+' 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 {c: 1, b: 1, v: 2, x: 2}, what is the expected number of times the pattern 'x*v' appears? 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 {s: 2, t: 3, c: 1}. What is the expected number of occurrences of the pattern 't.*c' 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 {v: 1, d: 2, y: 1, h: 1, m: 1}. What is the expected number of occurrences of the pattern 'v*h' 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 {m: 3, p: 3} 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"
}
] | 0.6 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {d: 1, s: 1, g: 1, o: 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 {z: 2, b: 4}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 5, n: 1}, what is the expected number of times the pattern 'cn+' 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 3 letters from the multiset {l: 1, q: 4, p: 1}. What is the expected number of occurrences of the pattern 'q+l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.37 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, b: 5}, 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {d: 1, c: 5} 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {l: 2, p: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'q*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.7 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, u: 1, x: 1, y: 3}, what is the expected number of times the pattern 'x*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.7 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {m: 1, e: 1, r: 3, d: 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": "When randomly selecting 3 letters from the multiset {r: 3, z: 3} to form a word, what is the expected number of matches of the pattern 'r+z'? 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 {k: 1, n: 2, r: 1, i: 1, j: 1}. What is the expected number of occurrences of the pattern 'ij*' 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 {b: 3, a: 1, m: 2}, what is the expected number of times the pattern 'ma+' 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 {z: 3, j: 3} 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}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {c: 4, u: 2} to form a word, what is the expected number of matches of the pattern 'u+c'? 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 {a: 1, r: 1, v: 3, u: 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"
}
] | 0.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, p: 1, m: 1, r: 1}, what is the expected number of times the pattern 'hm*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.7 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {w: 4, d: 2} to form a word, what is the expected number of matches of the pattern 'w+d'? 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 {r: 1, q: 3, y: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, k: 3}, what is the expected number of times the pattern 'k.*h' appears? Round 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 {t: 1, v: 3, s: 1, n: 1}. What is the expected number of occurrences of the pattern 'ns+' 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 {k: 4, s: 2}, 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"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {t: 2, s: 1, h: 2, i: 1}. 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}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, w: 1, b: 1, i: 1, y: 2}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
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