messages listlengths 1 1 | ground_truth stringclasses 13
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {j: 2, l: 2}. What is the expected number of occurrences of the pattern 'jl+' in each word? Round your answer 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 2 by randomly selecting letters from the multiset {r: 1, s: 1, d: 2}, what is the expected number of times the pattern 'r*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 1, m: 1, d: 2}, what is the expected number of times the pattern 'd+m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 2, v: 2}, what is the expected number of times the pattern 'vy*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {l: 3, y: 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"
}
] | 0.5 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 1, h: 1, i: 1, c: 1}, 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": "When randomly selecting 2 letters from the multiset {w: 1, a: 1, j: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'y*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {u: 1, y: 1, x: 1, l: 1}. What is the expected number of occurrences of the pattern 'y.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {y: 1, b: 1, n: 1, i: 1}. What is the expected number of occurrences of the pattern 'ny*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {z: 1, y: 2, u: 1}. What is the expected number of occurrences of the pattern 'u+y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {v: 1, w: 1, n: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'wv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {t: 3, x: 1} to form a word, what is the expected number of matches of the pattern 'x*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.75 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {q: 2, r: 2}. 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"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {x: 1, d: 2, v: 1} to form a word, what is the expected number of matches of the pattern 'xd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.67 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {c: 3, b: 1}. What is the expected number of occurrences of the pattern 'c.*c' 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 2 letters from the multiset {d: 1, v: 1, o: 1, g: 1}. What is the expected number of occurrences of the pattern 'd.*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {g: 2, r: 2}. 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"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {w: 1, p: 1, f: 1, i: 1}. What is the expected number of occurrences of the pattern 'if*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 2, k: 2}, what is the expected number of times the pattern 'hk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 2, s: 1, a: 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"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {w: 1, r: 1, l: 1, z: 1}. What is the expected number of occurrences of the pattern 'lw+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 1, z: 2, w: 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {e: 1, r: 1, a: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'a+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 1, a: 2, f: 1}, what is the expected number of times the pattern 'fa*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.67 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 2, j: 1, s: 1}, what is the expected number of times the pattern 'jc*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.67 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 1, h: 1, u: 1, y: 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": "Form a word by randomly choosing 2 letters from the multiset {s: 1, z: 1, o: 1, n: 1}. What is the expected number of occurrences of the pattern 'on+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 1, a: 3}, 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {w: 2, u: 2} 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"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {h: 1, c: 1, t: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'tc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {j: 1, m: 1, x: 1, n: 1}. What is the expected number of occurrences of the pattern 'j+m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 1, t: 1, r: 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 1, a: 2, q: 1}, what is the expected number of times the pattern 'aq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 2, a: 2}, what is the expected number of times the pattern 'w*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {u: 1, y: 1, g: 1, 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"
}
] | 0.08 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {r: 1, k: 1, w: 1, p: 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": "Form a word by randomly choosing 2 letters from the multiset {t: 1, k: 1, o: 1, i: 1}. What is the expected number of occurrences of the pattern 'k*i' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {f: 1, e: 1, h: 1, v: 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": "When randomly selecting 2 letters from the multiset {j: 1, c: 2, o: 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"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 2, f: 2}, what is the expected number of times the pattern 'g+f' 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 2 by randomly selecting letters from the multiset {c: 2, n: 1, z: 1}, what is the expected number of times the pattern 'z*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {i: 1, t: 2, v: 1}. What is the expected number of occurrences of the pattern 'it+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {e: 1, p: 1, g: 1, h: 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 2 by randomly selecting letters from the multiset {j: 2, w: 2}, what is the expected number of times the pattern 'wj*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {m: 2, f: 2}. What is the expected number of occurrences of the pattern 'fm+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {x: 1, o: 3} 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"
}
] | 0.5 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {o: 1, p: 1, t: 2} 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"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {b: 1, c: 1, m: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'mb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {y: 1, i: 1, f: 1, d: 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": "When randomly selecting 2 letters from the multiset {d: 2, t: 2} 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"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {t: 1, y: 3} to form a word, what is the expected number of matches of the pattern 'yt*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.75 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 1, i: 3}, what is the expected number of times the pattern 'ri+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {b: 3, l: 1} to form a word, what is the expected number of matches of the pattern 'l.*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {m: 1, g: 3} to form a word, what is the expected number of matches of the pattern 'mg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.75 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {r: 1, l: 2, f: 1} to form a word, what is the expected number of matches of the pattern 'f+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 1, c: 3}, what is the expected number of times the pattern 'c.*u' 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 2 letters from the multiset {t: 1, p: 1, b: 2}. What is the expected number of occurrences of the pattern 'tb+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {n: 1, j: 1, r: 1, o: 1}. What is the expected number of occurrences of the pattern 'j+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {i: 3, l: 1}, what is the expected number of times the pattern 'l*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.75 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 2, k: 2}, what is the expected number of times the pattern 'k*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {n: 1, i: 1, d: 1, s: 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {c: 1, m: 1, d: 1, x: 1} 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"
}
] | 0.58 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {e: 1, r: 1, y: 1, h: 1}. 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 2, k: 1, 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 2 by randomly selecting letters from the multiset {y: 1, e: 1, d: 1, n: 1}, what is the expected number of times the pattern 'e+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 1, a: 1, z: 2}, what is the expected number of times the pattern 'z.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {h: 1, m: 1, g: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? 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 2 letters from the multiset {c: 3, i: 1}. What is the expected number of occurrences of the pattern 'ci*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.75 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {b: 1, k: 1, t: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'y+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 1, m: 1, b: 1, c: 1}, what is the expected number of times the pattern 'hh*' 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 2 letters from the multiset {j: 1, u: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'j*z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 1, w: 1, t: 1, u: 1}, what is the expected number of times the pattern 'd.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {d: 1, z: 1, n: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'w+z'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {s: 1, y: 2, c: 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"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {x: 3, f: 1}. 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"
}
] | 1.75 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 1, k: 1, r: 2}, what is the expected number of times the pattern 'm*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {r: 1, q: 1, d: 1, m: 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 2 letters from the multiset {g: 1, s: 1, m: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {w: 1, y: 1, v: 2}. What is the expected number of occurrences of the pattern 'vw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {k: 1, i: 1, q: 1, z: 1} to form a word, what is the expected number of matches of the pattern 'qz+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {s: 1, e: 1, z: 1, a: 1}. What is the expected number of occurrences of the pattern 'as*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {i: 1, c: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'c*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.67 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {s: 1, t: 2, q: 1} to form a word, what is the expected number of matches of the pattern 's*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 1, p: 1, b: 1, v: 1}, what is the expected number of times the pattern 'p.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {k: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'o+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {x: 3, r: 1} to form a word, what is the expected number of matches of the pattern 'r*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.75 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {e: 1, q: 1, g: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'q.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {c: 2, b: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {d: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'db+'? 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 2 letters from the multiset {n: 1, t: 1, a: 1, p: 1}. What is the expected number of occurrences of the pattern 't*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {q: 1, y: 1, d: 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"
}
] | 0.58 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 1, u: 1, m: 2}, what is the expected number of times the pattern 'eu+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {l: 3, n: 1}, what is the expected number of times the pattern 'l+n' 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 2 letters from the multiset {i: 2, y: 1, e: 1}. What is the expected number of occurrences of the pattern 'yi+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {k: 3, y: 1}. What is the expected number of occurrences of the pattern 'k*y' 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 2 letters from the multiset {q: 1, s: 1, v: 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"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {h: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'n.*h'? 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 2 letters from the multiset {c: 1, h: 3}. What is the expected number of occurrences of the pattern 'h*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.75 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {a: 2, h: 2}, what is the expected number of times the pattern 'ha*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {c: 1, n: 1, p: 1, k: 1}. What is the expected number of occurrences of the pattern 'n*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
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