messages list | ground_truth string | dataset string |
|---|---|---|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {c: 1, e: 5, f: 2, n: 3}. What is the expected number of occurrences of the pattern 'n*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.92 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {q: 10, h: 3} 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"
}
] | 5.77 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {p: 6, c: 4} to form a word, what is the expected number of matches of the pattern 'p*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.8 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 1, n: 3, x: 3, z: 1, p: 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 4, q: 4, b: 6}. What is the expected number of occurrences of the pattern 'q*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.18 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 5, d: 4, t: 5}, 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"
}
] | 0.66 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 5, p: 5, i: 4}. What is the expected number of occurrences of the pattern 'p.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.66 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 3, o: 4, u: 5}, what is the expected number of times the pattern 'o+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.46 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 4, z: 3, d: 4, v: 2}, what is the expected number of times the pattern 'z*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.49 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 2, f: 2, i: 3, v: 4, b: 3}, 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"
}
] | 0.14 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {w: 1, b: 3, g: 6, r: 3, t: 2}. What is the expected number of occurrences of the pattern 'g.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.34 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {p: 4, l: 3, h: 1, z: 2, r: 2}. What is the expected number of occurrences of the pattern 'z*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.96 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 3, y: 1, f: 7, n: 2, u: 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"
}
] | 0.63 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {h: 5, k: 4, i: 3, x: 2, b: 1}. What is the expected number of occurrences of the pattern 'k*b' 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 4 letters from the multiset {j: 2, i: 4, v: 2, o: 2, q: 1} to form a word, what is the expected number of matches of the pattern 'j.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.22 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 8, h: 6}, 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"
}
] | 1.85 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {k: 3, s: 2, p: 3, c: 7}. 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"
}
] | 1.58 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {k: 4, n: 1, o: 1, e: 3, c: 5} to form a word, what is the expected number of matches of the pattern 'k+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.11 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {g: 3, r: 5, j: 2, x: 4} 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"
}
] | 0.33 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {f: 8, d: 4} to form a word, what is the expected number of matches of the pattern 'fd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.56 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {g: 3, s: 3, u: 2, f: 2, n: 1} to form a word, what is the expected number of matches of the pattern 'g*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.17 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {j: 4, d: 6} to form a word, what is the expected number of matches of the pattern 'jd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.83 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {n: 4, f: 2, p: 2, s: 1, j: 2}. 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"
}
] | 0.18 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 7, v: 3}. What is the expected number of occurrences of the pattern 'z*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.37 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {t: 2, h: 2, z: 5, o: 4, x: 2} to form a word, what is the expected number of matches of the pattern 'o+t'? 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 4 letters from the multiset {k: 4, n: 4, e: 4, j: 2}. What is the expected number of occurrences of the pattern 'j+e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.14 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 3, w: 3, x: 4, e: 2}, what is the expected number of times the pattern 'x+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.46 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {a: 4, p: 3, f: 2, v: 3}. What is the expected number of occurrences of the pattern 'av*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.09 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 6, x: 8}. 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"
}
] | 1.85 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {b: 1, c: 4, r: 3, y: 3}. What is the expected number of occurrences of the pattern 'b.*b' 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 5 by randomly selecting letters from the multiset {v: 8, y: 6}, what is the expected number of times the pattern 'y.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.65 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 7, i: 6}, what is the expected number of times the pattern 'i*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.26 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 5, c: 4, a: 1, e: 4}, what is the expected number of times the pattern 'y*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.56 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 3, z: 7}, what is the expected number of times the pattern 'z+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.18 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 1, t: 2, p: 3, w: 4, j: 4}, what is the expected number of times the pattern 'w+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.23 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 6, u: 3, t: 2, x: 1, i: 2}, what is the expected number of times the pattern 'w+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.18 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {u: 2, m: 2, a: 1, c: 2, v: 6}. What is the expected number of occurrences of the pattern 'a*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.96 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 2, u: 4, a: 2, h: 4}, what is the expected number of times the pattern 't*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.96 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {g: 4, n: 5, q: 2, s: 3} to form a word, what is the expected number of matches of the pattern 'q*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.28 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {b: 8, z: 4}. What is the expected number of occurrences of the pattern 'z+b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.22 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {n: 5, o: 7, t: 3} to form a word, what is the expected number of matches of the pattern 'n.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.71 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 5, h: 2, n: 3}. 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"
}
] | 1.9 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {s: 6, l: 4} to form a word, what is the expected number of matches of the pattern 'sl*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.43 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {n: 1, e: 5, a: 4, x: 2, u: 1} to form a word, what is the expected number of matches of the pattern 'e+x'? 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 5 letters from the multiset {c: 9, z: 4}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.77 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {e: 4, l: 5, m: 5} to form a word, what is the expected number of matches of the pattern 'l*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 3, k: 3, z: 2, g: 3, r: 2}, what is the expected number of times the pattern 'gr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.12 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 4, r: 2, g: 3, z: 4, n: 2}, what is the expected number of times the pattern 'zd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.36 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {a: 5, f: 2, i: 2, o: 3, g: 2}. What is the expected number of occurrences of the pattern 'a.*f' 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 5 by randomly selecting letters from the multiset {n: 7, f: 6}, what is the expected number of times the pattern 'f*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.25 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 3, z: 6, o: 2, t: 3}, what is the expected number of times the pattern 'w*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.86 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {n: 6, b: 4, d: 4} to form a word, what is the expected number of matches of the pattern 'n*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.17 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {g: 5, b: 6}. What is the expected number of occurrences of the pattern 'gg*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.21 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 6, h: 7}, what is the expected number of times the pattern 'ht*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.25 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {m: 4, t: 2, k: 2, r: 3} to form a word, what is the expected number of matches of the pattern 'm*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.93 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {p: 4, h: 7} to form a word, what is the expected number of matches of the pattern 'h.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.53 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 3, y: 3, g: 6}. What is the expected number of occurrences of the pattern 'g*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.58 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, a: 1, c: 3, m: 4, o: 4}, 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"
}
] | 0.53 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 2, s: 2, l: 1, m: 5, c: 2}, 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"
}
] | 0.91 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {d: 4, i: 2, o: 3, b: 4, w: 1}, what is the expected number of times the pattern 'wi*' 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 4 letters from the multiset {l: 1, h: 4, f: 3, m: 2, s: 5}. What is the expected number of occurrences of the pattern 'h*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.67 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {b: 8, t: 4} 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"
}
] | 0.31 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 3, a: 3, i: 3, v: 5}, what is the expected number of times the pattern 'c+a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.22 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 3, e: 2, a: 4, q: 4, h: 2}, what is the expected number of times the pattern 'q*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.67 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {s: 5, o: 6} to form a word, what is the expected number of matches of the pattern 'so+'? 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 4 by randomly selecting letters from the multiset {r: 4, e: 4, w: 2, c: 2, f: 1}, what is the expected number of times the pattern 'c*e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.39 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {j: 3, e: 4, r: 3}. 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"
}
] | 0.8 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {w: 7, h: 5}, what is the expected number of times the pattern 'wh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.46 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {w: 4, f: 2, p: 4, a: 1}. What is the expected number of occurrences of the pattern 'f.*p' 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": "If you form a word of length 5 by randomly selecting letters from the multiset {q: 3, o: 8}, 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"
}
] | 5.09 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {g: 7, v: 7} to form a word, what is the expected number of matches of the pattern 'v*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.14 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {d: 7, s: 4, y: 3} to form a word, what is the expected number of matches of the pattern 'y+s'? 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 4 letters from the multiset {z: 1, v: 1, e: 3, a: 3, d: 2}. What is the expected number of occurrences of the pattern 'ed*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.42 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {b: 7, o: 7}. What is the expected number of occurrences of the pattern 'o.*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.38 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {e: 5, d: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'e+d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.52 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 5, t: 4, v: 2}. What is the expected number of occurrences of the pattern 'tv+' 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": "Form a word by randomly choosing 4 letters from the multiset {w: 7, v: 5}. 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"
}
] | 1.91 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 4, p: 3, d: 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"
}
] | 0.8 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {o: 7, r: 5}, what is the expected number of times the pattern 'r.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.59 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 2, v: 2, f: 4, m: 2, k: 2}. What is the expected number of occurrences of the pattern 'mv+' 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 4 by randomly selecting letters from the multiset {m: 6, i: 6}, what is the expected number of times the pattern 'mi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.15 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {g: 6, r: 5}, 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"
}
] | 1.82 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 6, r: 3, j: 4}, what is the expected number of times the pattern 'r*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.24 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 4, i: 3, o: 3} 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"
}
] | 0.67 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 3, r: 3, y: 4, b: 1}, what is the expected number of times the pattern 'lr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.38 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {n: 6, e: 5, b: 4}. What is the expected number of occurrences of the pattern 'e.*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.95 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {k: 6, p: 5}. What is the expected number of occurrences of the pattern 'k.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.64 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {r: 7, f: 4} 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"
}
] | 0.65 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 1, t: 2, z: 5, q: 5}, what is the expected number of times the pattern 'q+e' 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 4 letters from the multiset {x: 8, w: 5}. 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"
}
] | 2.15 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {g: 5, i: 4, y: 6} to form a word, what is the expected number of matches of the pattern 'iy*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.51 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {e: 10, f: 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"
}
] | 2.57 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {w: 3, q: 3, f: 3, c: 2} 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"
}
] | 0.11 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 9, x: 3}, what is the expected number of times the pattern 't.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.05 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {i: 3, c: 3, v: 3, e: 3, y: 2} to form a word, what is the expected number of matches of the pattern 've+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.22 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {d: 4, e: 3, j: 3} 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"
}
] | 1.33 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 2, x: 2, f: 4, s: 4, a: 3}, what is the expected number of times the pattern 'x.*a' 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 4 letters from the multiset {y: 4, q: 3, j: 5} to form a word, what is the expected number of matches of the pattern 'yj+'? 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 4 by randomly selecting letters from the multiset {o: 3, l: 3, f: 5, u: 2}, 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"
}
] | 0.23 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 6, x: 5}, 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"
}
] | 1.09 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.