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 {c: 3, a: 1, q: 1, l: 1}. What is the expected number of occurrences of the pattern 'l.*q' 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 {p: 3, x: 3}. What is the expected number of occurrences of the pattern 'p*x' in each word? Round your answer 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 {k: 1, o: 1, u: 1, c: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'c*f'? 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: 1, w: 2, o: 2, i: 1}, what is the expected number of times the pattern 'co+' appears? 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: 1, g: 2, e: 2, u: 1}. What is the expected number of occurrences of the pattern 'gy+' 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 {z: 3, k: 3}, what is the expected number of times the pattern 'z*k' 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 {z: 2, i: 1, d: 1, w: 2}, what is the expected number of times the pattern 'i*z' appears? Round 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 {g: 1, x: 1, b: 3, o: 1}. What is the expected number of occurrences of the pattern 'g+o' 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 {m: 4, a: 2} to form a word, what is the expected number of matches of the pattern 'ma+'? 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 {n: 1, r: 2, t: 1, j: 1, s: 1} to form a word, what is the expected number of matches of the pattern 'r.*t'? 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 {n: 1, a: 2, x: 3} to form a word, what is the expected number of matches of the pattern 'xa+'? 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 {r: 1, o: 1, a: 1, m: 3} to form a word, what is the expected number of matches of the pattern 'r+m'? 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 {j: 1, a: 1, r: 2, n: 1, y: 1}. What is the expected number of occurrences of the pattern 'n*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 {d: 5, g: 1}, what is the expected number of times the pattern 'dg*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.83 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 1, c: 1, k: 1, n: 2, u: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {g: 1, j: 1, h: 1, c: 2, k: 1}. What is the expected number of occurrences of the pattern 'c.*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 {w: 1, u: 4, h: 1} to form a word, what is the expected number of matches of the pattern 'w*h'? 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 {x: 1, w: 1, y: 2, n: 1, m: 1} to form a word, what is the expected number of matches of the pattern 'n+m'? 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 {p: 2, s: 1, u: 1, m: 1, k: 1}. What is the expected number of occurrences of the pattern 'ks+' 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 {c: 2, b: 2, o: 1, n: 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"
}
] | 0.5 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {s: 2, u: 2, m: 1, r: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, u: 3, t: 1, m: 1}, what is the expected number of times the pattern 'u*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.75 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {t: 1, c: 2, o: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'z.*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, x: 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"
}
] | 1.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, b: 1, c: 1, i: 1, u: 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"
}
] | 0.5 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, b: 4}, 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"
}
] | 1.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 1, i: 1, z: 1, w: 2, j: 1}, what is the expected number of times the pattern 'wz*' 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 {t: 3, x: 1, z: 1, d: 1}, what is the expected number of times the pattern 'z*t' appears? 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 {u: 1, y: 1, t: 2, m: 1, x: 1}, what is the expected number of times the pattern 'y*t' appears? Round 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 {j: 4, c: 2} to form a word, what is the expected number of matches of the pattern 'jc+'? 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 {g: 2, f: 2, j: 2}. What is the expected number of occurrences of the pattern 'jg*' 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": "Form a word by randomly choosing 3 letters from the multiset {y: 2, c: 2, g: 2}. What is the expected number of occurrences of the pattern 'yc+' 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": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 4, m: 2}, what is the expected number of times the pattern 'a.*a' appears? Round 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 {v: 1, d: 1, s: 1, u: 2, a: 1}, what is the expected number of times the pattern 'ds*' 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 {f: 2, w: 4}. What is the expected number of occurrences of the pattern 'f.*w' 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": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 3, n: 3}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {r: 1, j: 1, e: 1, c: 3} to form a word, what is the expected number of matches of the pattern 'e+c'? 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 {e: 1, r: 1, w: 1, g: 2, p: 1}, what is the expected number of times the pattern 'e+g' 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 {u: 1, o: 1, z: 2, i: 1, x: 1}, what is the expected number of times the pattern 'i*x' 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 {u: 2, d: 4} to form a word, what is the expected number of matches of the pattern 'u.*d'? 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 {d: 3, q: 3}. What is the expected number of occurrences of the pattern 'd+q' 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": "When randomly selecting 3 letters from the multiset {o: 1, a: 1, e: 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"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 2, n: 1, c: 1, v: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 2, o: 1, u: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'p.*o'? 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, y: 1, c: 2, p: 1} 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": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, d: 2, v: 1, s: 1, l: 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": "Form a word by randomly choosing 3 letters from the multiset {n: 1, s: 1, c: 1, v: 2, w: 1}. What is the expected number of occurrences of the pattern 's+w' 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 {q: 1, o: 1, y: 1, b: 3}. What is the expected number of occurrences of the pattern 'o*y' 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 {z: 5, d: 1}, what is the expected number of times the pattern 'z*d' appears? 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 {f: 4, v: 2} 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"
}
] | 1.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, f: 2, d: 3}. What is the expected number of occurrences of the pattern 'f+x' 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 {y: 1, x: 1, l: 3, d: 1} to form a word, what is the expected number of matches of the pattern 'l+d'? 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 {f: 1, h: 3, c: 2} to form a word, what is the expected number of matches of the pattern 'h*c'? Round 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 {i: 2, d: 2, o: 2}. What is the expected number of occurrences of the pattern 'o.*d' in each word? Round your answer 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 {c: 1, t: 2, n: 1, i: 2}. What is the expected number of occurrences of the pattern 'ic+' 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": "Form a word by randomly choosing 3 letters from the multiset {y: 2, o: 1, u: 3}. What is the expected number of occurrences of the pattern 'ou*' 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": "When randomly selecting 3 letters from the multiset {p: 4, s: 2} 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"
}
] | 1.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, m: 3, v: 1, w: 1}. What is the expected number of occurrences of the pattern 'vj*' 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": "Form a word by randomly choosing 3 letters from the multiset {b: 1, u: 2, y: 1, t: 1, e: 1}. 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": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, r: 1, e: 1, s: 1, v: 1}, what is the expected number of times the pattern 'qv*' 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 {g: 1, w: 2, l: 3}, what is the expected number of times the pattern 'l+g' 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 {w: 2, r: 4}. What is the expected number of occurrences of the pattern 'wr+' 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": "When randomly selecting 3 letters from the multiset {j: 1, u: 3, w: 2} to form a word, what is the expected number of matches of the pattern 'u.*w'? 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: 1, s: 1, z: 2, c: 1, k: 1}. What is the expected number of occurrences of the pattern 's*k' 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": "Form a word by randomly choosing 3 letters from the multiset {m: 1, b: 2, u: 2, c: 1}. What is the expected number of occurrences of the pattern 'uu+' 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": "Form a word by randomly choosing 3 letters from the multiset {p: 2, c: 3, l: 1}. What is the expected number of occurrences of the pattern 'c+p' 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 {a: 1, q: 2, h: 1, o: 2}. What is the expected number of occurrences of the pattern 'a+q' 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": "Form a word by randomly choosing 3 letters from the multiset {y: 2, s: 2, i: 1, k: 1}. What is the expected number of occurrences of the pattern 'y+k' 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 {k: 2, v: 1, i: 1, s: 2}. What is the expected number of occurrences of the pattern 's+k' 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, e: 5} 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"
}
] | 2.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, e: 1, i: 1, n: 2, m: 1}. What is the expected number of occurrences of the pattern 'ne+' 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 {k: 2, a: 4} to form a word, what is the expected number of matches of the pattern 'k.*a'? 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 {j: 2, x: 3, m: 1}, what is the expected number of times the pattern 'jm+' 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 {x: 2, p: 4} 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"
}
] | 1.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 2, k: 4}, what is the expected number of times the pattern 'ka*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 2, s: 3, r: 1}, what is the expected number of times the pattern 'sr*' appears? 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 {d: 1, x: 1, u: 1, q: 1, g: 2}, what is the expected number of times the pattern 'xd+' 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 {c: 1, j: 1, g: 2, z: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'jz+'? 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 {b: 1, x: 1, s: 2, z: 1, e: 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"
}
] | 1.13 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, f: 1, q: 3}, what is the expected number of times the pattern 'h*q' 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 {n: 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": "When randomly selecting 3 letters from the multiset {c: 1, o: 1, z: 1, w: 3} to form a word, what is the expected number of matches of the pattern 'cz+'? 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 {w: 1, t: 5} to form a word, what is the expected number of matches of the pattern 'wt+'? Round 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 {c: 2, g: 2, j: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'jg*'? 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 {r: 3, g: 3}, 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"
}
] | 0.6 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, f: 1, u: 1, r: 1, o: 1}. What is the expected number of occurrences of the pattern 'rf*' 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 {f: 1, p: 1, u: 1, a: 1, 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": "Form a word by randomly choosing 3 letters from the multiset {a: 2, x: 3, w: 1}. What is the expected number of occurrences of the pattern 'a.*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": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 2, s: 1, c: 2, y: 1}, what is the expected number of times the pattern 's.*i' 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 {a: 3, h: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'ha+'? 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 {t: 1, v: 1, c: 1, f: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'i.*t'? Round 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 {j: 3, b: 3}. 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"
}
] | 0.45 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, a: 1, m: 1, f: 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {s: 4, h: 2}. 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"
}
] | 0.6 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {q: 2, f: 1, o: 3}. 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"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, c: 1, b: 2}, what is the expected number of times the pattern 'f.*c' 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 {x: 2, n: 1, s: 1, j: 1, y: 1}, what is the expected number of times the pattern 'xn*' appears? Round 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 {p: 1, v: 2, d: 1, k: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'pk+'? 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 {f: 2, q: 1, x: 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"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, d: 1, p: 1, v: 2}, what is the expected number of times the pattern 'vd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
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