messages listlengths 1 1 | ground_truth stringclasses 126 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {b: 2, j: 4}. 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"
}
] | 3.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {e: 2, v: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'e.*v'? 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 {u: 2, v: 1, l: 3}. What is the expected number of occurrences of the pattern 'vu*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.65 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, i: 2}, what is the expected number of times the pattern 'i*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.33 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {b: 1, a: 1, h: 1, w: 1, n: 1} to form a word, what is the expected number of matches of the pattern 'na+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.05 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {k: 1, r: 2, n: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'nr*'? 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 {t: 2, m: 2, x: 2}, what is the expected number of times the pattern 'mt*' appears? 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 2 by randomly selecting letters from the multiset {u: 4, x: 1, w: 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"
}
] | 0.4 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {y: 3, t: 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"
}
] | 0.9 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, x: 1, b: 2, h: 1}. What is the expected number of occurrences of the pattern 'xo+' 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": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 3, e: 2, p: 1}, what is the expected number of times the pattern 'p+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 2 by randomly selecting letters from the multiset {b: 2, g: 1, k: 2, i: 1}, what is the expected number of times the pattern 'ib*' appears? 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 2 by randomly selecting letters from the multiset {a: 2, s: 2, t: 1}, what is the expected number of times the pattern 't.*s' 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 {a: 2, n: 3} to form a word, what is the expected number of matches of the pattern 'a.*a'? 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 2 letters from the multiset {y: 1, c: 1, i: 3}. 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {o: 1, v: 1, z: 1, g: 1, u: 1} to form a word, what is the expected number of matches of the pattern 'go+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.05 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {v: 2, a: 2}. What is the expected number of occurrences of the pattern 'va*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.33 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, m: 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"
}
] | 0.5 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {i: 1, x: 1, b: 1, u: 1}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {a: 2, c: 4} to form a word, what is the expected number of matches of the pattern 'ca+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {s: 2, d: 1, v: 1, i: 1, b: 1} 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"
}
] | 0.07 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 1, f: 1, w: 1, l: 1, o: 1}, what is the expected number of times the pattern 'w*f' appears? Round 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 {y: 2, p: 1, z: 1}, what is the expected number of times the pattern 'pz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.92 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {m: 2, z: 2, x: 1}. What is the expected number of occurrences of the pattern 'x.*z' 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 2 letters from the multiset {a: 1, k: 2, r: 1, d: 1}. What is the expected number of occurrences of the pattern 'd.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.05 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {c: 2, l: 3} to form a word, what is the expected number of matches of the pattern 'l.*c'? 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: 2, j: 2, r: 2} to form a word, what is the expected number of matches of the pattern 'jr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {s: 2, b: 1, x: 1, 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": "Form a word by randomly choosing 3 letters from the multiset {n: 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"
}
] | 0.6 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {a: 1, h: 1, w: 1, f: 1, s: 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 4, b: 1}, what is the expected number of times the pattern 'e*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {h: 1, j: 3, 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"
}
] | 0.07 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {z: 1, w: 2, n: 1}. What is the expected number of occurrences of the pattern 'w+z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.42 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {i: 1, r: 1, e: 1, f: 1, d: 1}, 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {s: 1, k: 1, d: 2, v: 1, y: 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"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {l: 3, y: 3} to form a word, what is the expected number of matches of the pattern 'l+y'? 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 {u: 3, i: 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"
}
] | 0.3 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {q: 3, f: 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"
}
] | 0.3 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, u: 2, s: 1}. What is the expected number of occurrences of the pattern 'u+s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.23 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {b: 1, c: 1, r: 2} to form a word, what is the expected number of matches of the pattern 'cb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.92 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {f: 1, t: 1, r: 1, w: 1, c: 1} to form a word, what is the expected number of matches of the pattern 'c*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.7 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {z: 2, v: 3}, what is the expected number of times the pattern 'v*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.1 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, z: 3}. What is the expected number of occurrences of the pattern 'o+z' 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": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 1, m: 1, o: 2, r: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 1, j: 5}, 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"
}
] | 0.33 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {u: 3, t: 2} to form a word, what is the expected number of matches of the pattern 'tu*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.1 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {w: 1, o: 1, f: 3, a: 1}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, u: 1, k: 1, j: 1, w: 1}. What is the expected number of occurrences of the pattern 'w*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.7 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 2, z: 2}, what is the expected number of times the pattern 'z.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {j: 1, w: 1, k: 3}. What is the expected number of occurrences of the pattern 'k*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.55 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {h: 2, o: 3, w: 1}. What is the expected number of occurrences of the pattern 'h.*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 2 letters from the multiset {r: 1, k: 1, l: 1, v: 1, u: 1}. What is the expected number of occurrences of the pattern 'kr*' 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": "When randomly selecting 2 letters from the multiset {u: 1, h: 2, z: 1} to form a word, what is the expected number of matches of the pattern 'zh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.67 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {l: 1, p: 1, s: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'ls*'? 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 {v: 1, o: 3, m: 2} to form a word, what is the expected number of matches of the pattern 'vm+'? 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 {c: 1, j: 2, g: 3}. What is the expected number of occurrences of the pattern 'cj*' 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 2 by randomly selecting letters from the multiset {s: 1, x: 2, q: 1, n: 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"
}
] | 0.07 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, c: 1, a: 2, n: 2}. What is the expected number of occurrences of the pattern 'c*a' 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": "When randomly selecting 3 letters from the multiset {x: 1, i: 1, z: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'iz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.92 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {g: 1, f: 1, u: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'g+j'? 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 {b: 1, f: 4} to form a word, what is the expected number of matches of the pattern 'fb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.8 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 3, a: 2} to form a word, what is the expected number of matches of the pattern 'pa*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.5 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {d: 1, f: 1, q: 1, i: 1} to form a word, what is the expected number of matches of the pattern 'fq+'? 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 {c: 1, q: 1, m: 1, n: 1, l: 1}. 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"
}
] | 0.45 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {c: 1, l: 1, r: 2, f: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'j+f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {d: 1, c: 1, x: 2} to form a word, what is the expected number of matches of the pattern 'dc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.92 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, d: 1, o: 1, i: 1}. What is the expected number of occurrences of the pattern 'd+i' 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, u: 3} to form a word, what is the expected number of matches of the pattern 'd*u'? 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 {z: 4, d: 2}. What is the expected number of occurrences of the pattern 'z.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.8 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, a: 2, d: 1}. What is the expected number of occurrences of the pattern 'nd+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {x: 3, p: 2}. 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"
}
] | 0.3 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {z: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 4, k: 1}, what is the expected number of times the pattern 'k.*e' 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 {e: 2, l: 2, u: 2}. What is the expected number of occurrences of the pattern 'l.*u' 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": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 3, d: 2}, what is the expected number of times the pattern 'd.*k' 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 2 by randomly selecting letters from the multiset {n: 1, m: 1, e: 2, i: 1, l: 1}, what is the expected number of times the pattern 'li+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.03 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {d: 1, s: 2, x: 1, b: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'ls*'? 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 2 by randomly selecting letters from the multiset {y: 1, v: 2, r: 1}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 1, b: 1, g: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'rb+'? 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 {u: 1, o: 1, k: 1, s: 1, h: 1} to form a word, what is the expected number of matches of the pattern 'u+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.05 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 1, c: 1, o: 1, i: 1, q: 1}, what is the expected number of times the pattern 's.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.05 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 2, e: 3} 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"
}
] | 0.9 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {p: 1, l: 1, x: 1, h: 1}. What is the expected number of occurrences of the pattern 'hl+' 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": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 2, b: 3}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {l: 1, x: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'x.*l'? 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 3 by randomly selecting letters from the multiset {d: 1, z: 1, q: 1, k: 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {y: 1, z: 2, u: 3}. 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"
}
] | 1.1 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 2, x: 3}, what is the expected number of times the pattern 'xv+' 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 2 letters from the multiset {j: 2, 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": "If you form a word of length 3 by randomly selecting letters from the multiset {u: 3, v: 2}, what is the expected number of times the pattern 'u+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.8 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {e: 1, z: 1, v: 1, y: 1, j: 2} to form a word, what is the expected number of matches of the pattern 'ej+'? 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 2 letters from the multiset {r: 1, j: 1, k: 1, s: 1}. What is the expected number of occurrences of the pattern 's.*s' 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 {r: 1, u: 1, c: 1, t: 1, h: 2}, what is the expected number of times the pattern 'u.*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.03 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {q: 2, b: 3, v: 1} to form a word, what is the expected number of matches of the pattern 'v.*q'? 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 {v: 2, n: 1, f: 1, o: 1}, what is the expected number of times the pattern 'on*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.7 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 2, y: 2, l: 2}, what is the expected number of times the pattern 'y+w' 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 2 letters from the multiset {w: 1, c: 1, x: 1, b: 1, 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: 2, d: 1, s: 2, l: 1}, what is the expected number of times the pattern 'd.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {k: 1, t: 1, d: 3}. 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"
}
] | 0.9 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {e: 1, b: 2, f: 2}. What is the expected number of occurrences of the pattern 'ee+' 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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