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 {z: 1, n: 1, h: 2, g: 2}. What is the expected number of occurrences of the pattern 'gn+' 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 {y: 2, f: 1, l: 1, v: 2}, what is the expected number of times the pattern 'f+v' 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 {n: 2, v: 2, z: 2}, what is the expected number of times the pattern 'nv+' 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 {c: 3, u: 1, p: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'pl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.57 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 2, r: 1, b: 1, c: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'cp*'? 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 {t: 1, h: 2, o: 1, x: 2} to form a word, what is the expected number of matches of the pattern 't+h'? 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 {y: 2, s: 1, k: 1, x: 1, e: 1}. What is the expected number of occurrences of the pattern 's*e' 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 {s: 3, c: 3}, 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"
}
] | 0.6 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {i: 2, e: 3, h: 1} 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"
}
] | 0.3 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, j: 1, g: 1, c: 3}, what is the expected number of times the pattern 'ck*' 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 {d: 1, y: 4, v: 1} 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 {q: 1, e: 1, i: 2, y: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'i+d'? 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 {w: 3, a: 2, o: 1}, what is the expected number of times the pattern 'ow+' 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 {f: 2, s: 1, j: 1, d: 2}. What is the expected number of occurrences of the pattern 'j+d' 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 {q: 2, a: 1, u: 1, i: 1, j: 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": "Form a word by randomly choosing 3 letters from the multiset {h: 1, r: 2, d: 1, n: 1, o: 1}. What is the expected number of occurrences of the pattern 'rn*' 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 {e: 2, w: 3, l: 1}. What is the expected number of occurrences of the pattern 'l*e' 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 {m: 4, r: 2}, what is the expected number of times the pattern 'm*r' appears? 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 {e: 4, o: 2}, 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"
}
] | 2.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, f: 3}, what is the expected number of times the pattern 'f+a' 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 {a: 1, x: 1, j: 2, m: 2}. 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {s: 4, v: 2} to form a word, what is the expected number of matches of the pattern 's.*v'? 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 {o: 3, m: 1, x: 2}, what is the expected number of times the pattern 'm*o' 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 {z: 1, q: 1, b: 3, m: 1} to form a word, what is the expected number of matches of the pattern 'q*m'? 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 {a: 2, l: 1, u: 1, z: 1, m: 1}, what is the expected number of times the pattern 'lm+' 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 {j: 1, n: 2, l: 2, k: 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"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 2, h: 1, n: 3}, what is the expected number of times the pattern 'h+j' 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 {u: 1, r: 2, s: 2, p: 1} to form a word, what is the expected number of matches of the pattern 'u*r'? 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 {q: 1, h: 1, k: 1, o: 2, d: 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": "Form a word by randomly choosing 3 letters from the multiset {z: 4, c: 1, q: 1}. 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"
}
] | 1.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {c: 5, e: 1}. What is the expected number of occurrences of the pattern 'e*c' in each word? Round your answer 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 {x: 2, s: 2, v: 2}, what is the expected number of times the pattern 'xs+' 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: 4, j: 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"
}
] | 1.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, o: 1, j: 1, p: 2}. What is the expected number of occurrences of the pattern 'op+' 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 {b: 3, t: 3}. 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"
}
] | 0.45 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 3, r: 3}, what is the expected number of times the pattern 'qr+' 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 {z: 1, t: 2, i: 1, u: 1, a: 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 {x: 2, y: 4}, 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"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, v: 1, i: 3}, 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": "When randomly selecting 3 letters from the multiset {i: 2, r: 1, g: 1, y: 1, o: 1} 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": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 4, d: 2}, what is the expected number of times the pattern 'u+d' appears? Round 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 {n: 1, f: 2, l: 3}. What is the expected number of occurrences of the pattern 'n+f' 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 {o: 2, d: 2, i: 1, q: 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": "When randomly selecting 3 letters from the multiset {r: 1, h: 3, i: 2} to form a word, what is the expected number of matches of the pattern 'h*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.5 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {w: 4, j: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'o.*w'? 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 {s: 1, l: 1, g: 3, j: 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"
}
] | 0.75 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {j: 1, d: 4, a: 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {g: 2, x: 4} to form a word, what is the expected number of matches of the pattern 'x*g'? 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 {h: 3, 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"
}
] | 0.9 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 1, o: 1, u: 2, m: 1, h: 1}, what is the expected number of times the pattern 'mu+' 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 {f: 1, r: 2, i: 2, n: 1}. What is the expected number of occurrences of the pattern 'nr+' 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 {j: 3, w: 3} to form a word, what is the expected number of matches of the pattern 'w*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.25 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, i: 1, y: 1, z: 1}. What is the expected number of occurrences of the pattern 'ez*' in each word? Round your answer 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, h: 3, g: 1, i: 1}, what is the expected number of times the pattern 'u.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {i: 3, o: 2, m: 1} to form a word, what is the expected number of matches of the pattern 'mi+'? 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 {v: 1, y: 2, e: 2, i: 1}, what is the expected number of times the pattern 'e.*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 {w: 4, e: 2}, 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"
}
] | 1.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, u: 5}, what is the expected number of times the pattern 'um+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 2, j: 1, g: 3}, what is the expected number of times the pattern 'g.*j' 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 {m: 3, u: 3} to form a word, what is the expected number of matches of the pattern 'm.*u'? 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 {p: 2, x: 2, h: 1, y: 1}. What is the expected number of occurrences of the pattern 'h+p' 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 {l: 1, v: 1, u: 4}, what is the expected number of times the pattern 'u.*l' 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 {y: 1, r: 1, f: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'i+f'? 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 {n: 1, l: 1, i: 1, s: 1, e: 2}. What is the expected number of occurrences of the pattern 'nl+' 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 {b: 2, h: 1, l: 1, c: 1, x: 1} 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, q: 1, f: 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 4, l: 2}, what is the expected number of times the pattern 'l+s' 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 {n: 2, q: 4}, what is the expected number of times the pattern 'q*n' 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 {u: 2, w: 3, z: 1}. What is the expected number of occurrences of the pattern 'z+u' 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: 2, z: 3, w: 1}, what is the expected number of times the pattern 'w.*z' 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 {j: 2, x: 4} to form a word, what is the expected number of matches of the pattern 'xj+'? 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: 3, d: 3}, what is the expected number of times the pattern 'dj*' appears? 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 {o: 1, p: 2, k: 1, e: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'kw+'? 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 {y: 2, t: 1, m: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'yk*'? 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 {m: 3, s: 1, o: 1, y: 1}. What is the expected number of occurrences of the pattern 's.*y' 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": "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 'lq+' 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 {n: 1, s: 1, k: 1, i: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'is*'? 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 {p: 1, w: 1, a: 1, g: 2, t: 1} to form a word, what is the expected number of matches of the pattern 'g+w'? 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 {w: 1, k: 2, g: 1, e: 2}, 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 {x: 1, l: 1, f: 1, e: 2, q: 1}. What is the expected number of occurrences of the pattern 'q*x' 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 {k: 3, m: 3}, what is the expected number of times the pattern 'k+m' 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 {w: 1, a: 2, f: 1, v: 1, c: 1}. What is the expected number of occurrences of the pattern 'af*' 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 {f: 3, i: 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 {l: 3, n: 2, j: 1}. What is the expected number of occurrences of the pattern 'nj+' 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 {c: 1, m: 1, j: 1, o: 1, d: 2} to form a word, what is the expected number of matches of the pattern 'dj+'? 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 {k: 3, z: 2, x: 1}, 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, n: 2, e: 2, g: 1}, what is the expected number of times the pattern 'i+n' 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 {v: 1, o: 2, u: 1, c: 1, f: 1}, what is the expected number of times the pattern 'fv+' 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 {e: 4, f: 2}, what is the expected number of times the pattern 'e+f' 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 {r: 2, p: 1, t: 1, m: 1, h: 1}, what is the expected number of times the pattern 'p+m' 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 {s: 1, d: 1, e: 1, v: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'sv+'? 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 {e: 2, w: 1, d: 1, k: 2}. What is the expected number of occurrences of the pattern 'we*' 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": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 1, r: 2, i: 1, 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"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, k: 2, q: 3}. 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"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, o: 2, n: 1, h: 1, q: 1}, what is the expected number of times the pattern 'qn+' 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: 4, e: 2}, what is the expected number of times the pattern 'te+' 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 {k: 1, r: 1, d: 1, s: 1, 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 {r: 2, i: 1, o: 1, k: 2} 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 {g: 1, n: 2, a: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'c.*a'? 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: 2, e: 1, f: 1, m: 1, c: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
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