messages list | ground_truth string | dataset string |
|---|---|---|
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {z: 3, p: 2, c: 5}. What is the expected number of occurrences of the pattern 'c+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 {r: 3, q: 1, k: 2, y: 2, h: 2}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, z: 1, r: 1, n: 2, v: 2}. What is the expected number of occurrences of the pattern 'xv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.18 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {p: 6, f: 1, v: 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {i: 2, m: 1, c: 1, z: 3, g: 1}, what is the expected number of times the pattern 'm.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.21 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 4, p: 6}, what is the expected number of times the pattern 'p.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.6 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {q: 1, v: 1, m: 1, n: 2, p: 3} to form a word, what is the expected number of matches of the pattern 'p+v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.12 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {t: 7, c: 5}. 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"
}
] | 0.95 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {h: 3, l: 9}. What is the expected number of occurrences of the pattern 'h.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.23 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {k: 3, s: 1, c: 4, j: 4} to form a word, what is the expected number of matches of the pattern 'kc+'? 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 {d: 1, y: 2, b: 2, t: 3, i: 4}, what is the expected number of times the pattern 'yd*' 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 {s: 4, y: 5, g: 3}, what is the expected number of times the pattern 'gy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.45 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {e: 3, z: 3, y: 5}. What is the expected number of occurrences of the pattern 'z*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {v: 2, o: 1, f: 4, y: 4} to form a word, what is the expected number of matches of the pattern 'f*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.72 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {d: 2, e: 1, p: 1, k: 4, s: 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"
}
] | 0.05 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, r: 3, t: 2, o: 1}. 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"
}
] | 0.08 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {v: 4, m: 1, o: 1, q: 2}. What is the expected number of occurrences of the pattern 'o*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.41 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {s: 5, e: 1, p: 3}. What is the expected number of occurrences of the pattern 'sp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.98 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {v: 2, p: 3, x: 1, j: 2, i: 4}. What is the expected number of occurrences of the pattern 'v.*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": "When randomly selecting 3 letters from the multiset {l: 3, y: 4, d: 2} to form a word, what is the expected number of matches of the pattern 'ld+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.18 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 3, k: 1, f: 5}, what is the expected number of times the pattern 'k.*k' 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 4 by randomly selecting letters from the multiset {u: 3, o: 2, b: 6}, what is the expected number of times the pattern 'b.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.64 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {z: 5, u: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'u*z'? Round 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 {l: 4, a: 2, z: 3} to form a word, what is the expected number of matches of the pattern 'al*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {y: 2, l: 3, v: 3} to form a word, what is the expected number of matches of the pattern 'y+l'? 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 3 letters from the multiset {x: 5, f: 4}. 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": "Form a word by randomly choosing 3 letters from the multiset {z: 5, u: 3}. What is the expected number of occurrences of the pattern 'u.*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.32 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {j: 3, e: 3, t: 2, q: 3, d: 1}, what is the expected number of times the pattern 'j*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.41 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 5, l: 4}, 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"
}
] | 0.83 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 4, j: 2, o: 3}, what is the expected number of times the pattern 'j+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.37 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 5, o: 4}, what is the expected number of times the pattern 'oh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.05 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {g: 3, b: 5}. 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"
}
] | 0.64 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 2, b: 2, v: 4, g: 3}. What is the expected number of occurrences of the pattern 'g*c' in each word? Round your answer 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 {d: 2, o: 3, y: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'y+g'? 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 4 letters from the multiset {j: 6, r: 3}. 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"
}
] | 1.5 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 6, n: 1, q: 3, r: 2}, what is the expected number of times the pattern 'n+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.14 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {m: 3, x: 6} to form a word, what is the expected number of matches of the pattern 'x.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.25 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {j: 1, n: 2, v: 2, y: 2, e: 3}. 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"
}
] | 0.13 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {a: 5, e: 4}. What is the expected number of occurrences of the pattern 'ae*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.34 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 4, s: 5}, 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"
}
] | 0.5 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {p: 3, w: 2, l: 3, n: 1, e: 3}. 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"
}
] | 0.6 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 4, m: 5}, what is the expected number of times the pattern 'ym+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.23 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {y: 4, e: 6} to form a word, what is the expected number of matches of the pattern 'ey+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.03 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {t: 2, n: 1, e: 2, k: 3} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, z: 4, a: 2, l: 1}, 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"
}
] | 0.67 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 1, t: 2, q: 2, c: 5, k: 2}, 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"
}
] | 0.91 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, s: 3, i: 3, o: 2}, 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"
}
] | 0.07 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {h: 5, m: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'k+h'? 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 {p: 2, f: 3, q: 6, c: 1}, what is the expected number of times the pattern 'cp*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.38 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 7, a: 5}, what is the expected number of times the pattern 'ao+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.69 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {a: 2, t: 2, g: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'ta*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.24 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, r: 4, f: 1, x: 3}, what is the expected number of times the pattern 'a*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.44 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {w: 2, c: 3, g: 5, d: 2}. What is the expected number of occurrences of the pattern 'g+w' 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": "When randomly selecting 4 letters from the multiset {n: 2, x: 6} to form a word, what is the expected number of matches of the pattern 'xn+'? 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 3 letters from the multiset {k: 6, d: 3}. What is the expected number of occurrences of the pattern 'kd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.57 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {g: 6, c: 2}. What is the expected number of occurrences of the pattern 'c*g' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.71 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {c: 4, b: 1, l: 3, x: 2}, what is the expected number of times the pattern 'cl*' appears? 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 {e: 2, r: 2, o: 5}. What is the expected number of occurrences of the pattern 'eo+' in each word? Round your answer 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 {l: 5, r: 1, k: 4, t: 1}. What is the expected number of occurrences of the pattern 'l.*l' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.09 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {e: 3, p: 2, i: 5}. What is the expected number of occurrences of the pattern 'p*e' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {y: 2, u: 3, d: 4, b: 2}, what is the expected number of times the pattern 'd.*b' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.44 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 1, g: 1, z: 2, e: 4, x: 1}, what is the expected number of times the pattern 'ez*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.57 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {y: 3, p: 3, o: 5} to form a word, what is the expected number of matches of the pattern 'po*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.15 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {b: 2, t: 3, n: 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"
}
] | 1.18 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {h: 5, y: 3, z: 3}. What is the expected number of occurrences of the pattern 'z.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.82 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, d: 3, e: 2, n: 2}. What is the expected number of occurrences of the pattern 'e.*j' 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 4 by randomly selecting letters from the multiset {q: 2, u: 3, l: 1, c: 1, e: 1}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 1, b: 4, n: 1, a: 3, k: 2}, what is the expected number of times the pattern 'a.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {r: 6, x: 4} 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"
}
] | 2.0 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {k: 2, b: 2, v: 4, s: 4}. 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"
}
] | 0.05 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {f: 2, h: 2, q: 3, e: 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"
}
] | 0.25 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 4, j: 3, h: 5}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.27 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {u: 3, s: 3, d: 4}. 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"
}
] | 0.4 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 2, w: 2, i: 3, t: 3}, what is the expected number of times the pattern 'wt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.24 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, r: 1, i: 4, v: 3}, what is the expected number of times the pattern 'm.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.16 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 9, q: 3}, what is the expected number of times the pattern 'q+v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.45 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {l: 1, d: 2, b: 1, x: 3, k: 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"
}
] | 0.21 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {v: 1, h: 3, g: 5} to form a word, what is the expected number of matches of the pattern 'vh+'? 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 {i: 6, w: 5}, 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"
}
] | 0.82 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 7, i: 4}, what is the expected number of times the pattern 'r+i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.21 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {e: 1, h: 2, o: 2, y: 3} to form a word, what is the expected number of matches of the pattern 'e*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.82 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {o: 2, p: 1, z: 3, e: 1, s: 1}. What is the expected number of occurrences of the pattern 'p+e' 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": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 1, w: 2, n: 1, s: 3, v: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {e: 2, b: 2, j: 4, a: 2}, what is the expected number of times the pattern 'ja*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.39 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 2, x: 1, d: 1, k: 4, g: 3}, what is the expected number of times the pattern 'k.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.44 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 2, s: 6}, 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"
}
] | 0.21 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {v: 3, b: 2, n: 2, q: 5}. What is the expected number of occurrences of the pattern 'vq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.02 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {a: 3, w: 2, p: 2, k: 2, e: 1} to form a word, what is the expected number of matches of the pattern 'k+e'? 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 4 letters from the multiset {a: 1, i: 3, z: 2, x: 4, w: 2}. What is the expected number of occurrences of the pattern 'xa*' 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": "When randomly selecting 4 letters from the multiset {h: 4, d: 7} to form a word, what is the expected number of matches of the pattern 'd.*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.53 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {j: 3, y: 2, f: 1, g: 2, z: 2}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, y: 3, w: 2, o: 2}, 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"
}
] | 0.32 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, p: 2, g: 2, a: 2, j: 1}, what is the expected number of times the pattern 'ap+' appears? 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 4 by randomly selecting letters from the multiset {f: 3, j: 2, a: 4, c: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 1, r: 3, h: 2, i: 5}, what is the expected number of times the pattern 'h.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.11 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {u: 3, y: 2, i: 3}. 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"
}
] | 0.4 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {y: 4, n: 6} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.0 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {a: 3, s: 4, i: 2} to form a word, what is the expected number of matches of the pattern 'as*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.0 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {y: 5, u: 4, t: 2} to form a word, what is the expected number of matches of the pattern 'y.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.55 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, j: 4, c: 2}, 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"
}
] | 0.08 | MATH |
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