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 {j: 2, k: 1, v: 1, y: 1, w: 1}, what is the expected number of times the pattern 'w+v' 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 {t: 3, p: 2, u: 1}, what is the expected number of times the pattern 'pu+' 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 {w: 1, z: 2, v: 3} to form a word, what is the expected number of matches of the pattern 'z*w'? 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 {e: 1, y: 1, s: 1, r: 1, j: 2}. What is the expected number of occurrences of the pattern 'e.*e' 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 {g: 1, y: 2, n: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'f.*f'? 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 {m: 1, j: 3, h: 1, i: 1}, what is the expected number of times the pattern 'm.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {c: 5, r: 1} to form a word, what is the expected number of matches of the pattern 'r+c'? 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 {a: 2, l: 2, n: 1, s: 1}. What is the expected number of occurrences of the pattern 'a*s' in each word? Round your answer 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 {v: 2, f: 4}. What is the expected number of occurrences of the pattern 'vf*' 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 {i: 2, r: 4}, what is the expected number of times the pattern 'i.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.8 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, f: 1, s: 1}, what is the expected number of times the pattern 'sc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.37 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {e: 2, a: 2, i: 2}. What is the expected number of occurrences of the pattern 'ai+' 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": "When randomly selecting 3 letters from the multiset {v: 1, s: 1, a: 2, e: 1, m: 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}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {d: 1, l: 1, w: 2, i: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'li*'? 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 {n: 1, t: 2, m: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'd.*n'? 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 {c: 3, i: 1, x: 2} 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"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 1, n: 1, m: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'pn*'? 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 {l: 1, i: 1, f: 1, d: 1, x: 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}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {a: 5, p: 1} to form a word, what is the expected number of matches of the pattern 'a+p'? 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 3 by randomly selecting letters from the multiset {b: 3, k: 1, v: 1, o: 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": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, a: 2, g: 1, n: 2}, what is the expected number of times the pattern 'gn+' 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 {v: 2, t: 2, o: 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"
}
] | 0.4 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, m: 1, w: 2, s: 1, v: 1}, what is the expected number of times the pattern 'aw+' 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 {d: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'd.*v'? 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 {a: 3, f: 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": "When randomly selecting 3 letters from the multiset {z: 3, f: 2, r: 1} 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, p: 1, h: 3}, what is the expected number of times the pattern 'p.*h' appears? 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 {h: 2, y: 2, v: 2}. 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"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {n: 1, c: 2, h: 3} to form a word, what is the expected number of matches of the pattern 'h.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, t: 1, m: 4}, 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 3 letters from the multiset {i: 2, t: 4}. What is the expected number of occurrences of the pattern 't.*i' 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": "When randomly selecting 3 letters from the multiset {n: 1, p: 2, v: 1, q: 1, d: 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"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {m: 1, w: 3, k: 2} to form a word, what is the expected number of matches of the pattern 'm+k'? 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 {c: 3, f: 3} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round 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 {o: 4, r: 2}. What is the expected number of occurrences of the pattern 'o.*o' 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": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 2, y: 2, v: 2}, 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}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {v: 1, d: 2, o: 1, t: 1, p: 1} 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {j: 1, y: 2, r: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'y*r'? 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 {u: 1, i: 1, k: 1, t: 2, m: 1}, what is the expected number of times the pattern 'm*t' appears? 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 {d: 2, r: 2, q: 2}, what is the expected number of times the pattern 'q*d' 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 {z: 2, h: 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": "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 'u.*u'? 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, c: 1, m: 1, f: 1, j: 1}, what is the expected number of times the pattern 'mp*' 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 {c: 3, b: 3}, what is the expected number of times the pattern 'cc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.95 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {q: 3, h: 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"
}
] | 0.6 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {i: 2, r: 1, j: 1, h: 1, t: 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": "Form a word by randomly choosing 3 letters from the multiset {s: 1, u: 2, y: 1, a: 1, k: 1}. What is the expected number of occurrences of the pattern 'yk*' 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 {w: 2, t: 3, n: 1}, what is the expected number of times the pattern 't+n' 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 3 by randomly selecting letters from the multiset {x: 2, f: 4}, what is the expected number of times the pattern 'f*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.73 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {j: 4, x: 2} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {a: 1, x: 2, j: 3}. What is the expected number of occurrences of the pattern 'xj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.5 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, h: 1, s: 2, c: 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": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, m: 1, v: 1, l: 3}, what is the expected number of times the pattern 'lv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.7 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, w: 1, y: 2, t: 2}. What is the expected number of occurrences of the pattern 'tl*' 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 {y: 2, o: 2, c: 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"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, z: 1, q: 1, l: 1, o: 1}, what is the expected number of times the pattern 'q.*q' 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 {m: 3, t: 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 {w: 1, e: 4, i: 1} to form a word, what is the expected number of matches of the pattern 'i.*e'? 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: 1, v: 2, l: 1, m: 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}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, d: 2, q: 1, n: 1, o: 1}, what is the expected number of times the pattern 'no*' 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 {o: 2, j: 4}, what is the expected number of times the pattern 'o+j' 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 {r: 2, o: 2, e: 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"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, y: 1, v: 1, f: 1, t: 1}, what is the expected number of times the pattern 'f.*b' 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 {i: 2, r: 2, x: 2}, 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": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, o: 1, v: 2, e: 1, l: 1}, what is the expected number of times the pattern 'o+e' 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 {z: 2, y: 4}, what is the expected number of times the pattern 'z*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.6 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, b: 3, x: 1, s: 1}. 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {o: 1, l: 1, f: 4} to form a word, what is the expected number of matches of the pattern 'of+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.37 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {s: 4, q: 2}. What is the expected number of occurrences of the pattern 'q.*s' 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": "When randomly selecting 3 letters from the multiset {d: 1, e: 1, q: 2, f: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'eq*'? 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: 1, k: 2, w: 1, b: 1, v: 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}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, g: 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}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, n: 3}, 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}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, e: 4}, what is the expected number of times the pattern 'e*l' 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 {s: 3, y: 3}. What is the expected number of occurrences of the pattern 'y+s' 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 {z: 1, i: 3, g: 1, c: 1}. What is the expected number of occurrences of the pattern 'z+c' 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 {c: 3, k: 3} to form a word, what is the expected number of matches of the pattern 'kc*'? 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 {i: 2, a: 2, b: 1, t: 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 1, x: 1, b: 2, n: 1, j: 1}, 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": "Form a word by randomly choosing 3 letters from the multiset {f: 1, t: 1, y: 2, q: 2}. What is the expected number of occurrences of the pattern 'y+q' 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": "When randomly selecting 3 letters from the multiset {w: 1, j: 1, a: 1, d: 2, n: 1} 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"
}
] | 0.57 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {k: 1, n: 2, p: 1, d: 1, l: 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, d: 3, z: 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"
}
] | 0.6 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {m: 3, x: 2, w: 1} to form a word, what is the expected number of matches of the pattern 'x.*w'? 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 {o: 3, k: 3}. What is the expected number of occurrences of the pattern 'o.*k' 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": "When randomly selecting 3 letters from the multiset {l: 1, r: 1, q: 2, p: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'l.*l'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, k: 3, q: 1, p: 1}, what is the expected number of times the pattern 'p+d' 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 {y: 2, o: 2, s: 2}, what is the expected number of times the pattern 'y+s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, b: 3}, what is the expected number of times the pattern 'q*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.95 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {u: 1, w: 2, k: 2, q: 1}. 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"
}
] | 0.07 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, b: 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": "When randomly selecting 3 letters from the multiset {z: 2, k: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'dk*'? 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 {a: 2, m: 1, i: 1, n: 2}, what is the expected number of times the pattern 'a.*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 {h: 1, o: 3, v: 2}, what is the expected number of times the pattern 'o*h' 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 {g: 1, v: 2, a: 1, k: 1, i: 1}. What is the expected number of occurrences of the pattern 'k.*a' 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 {p: 1, w: 1, n: 1, m: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'wm+'? 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: 2, k: 1, l: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'kl+'? 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 {e: 2, b: 2, n: 1, u: 1}. 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"
}
] | 0.5 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {o: 1, f: 1, r: 2, q: 1, z: 1} 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"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {u: 2, z: 1, q: 1, m: 1, w: 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 |
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