messages list | ground_truth string | dataset string |
|---|---|---|
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 7, o: 4}, what is the expected number of times the pattern 'o*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.5 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {t: 3, e: 3, o: 2, v: 2} to form a word, what is the expected number of matches of the pattern 'e+t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.48 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {n: 5, t: 2, z: 1, r: 4, f: 2}. What is the expected number of occurrences of the pattern 'n.*n' 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": "Form a word by randomly choosing 4 letters from the multiset {z: 2, x: 5, j: 3}. What is the expected number of occurrences of the pattern 'zj*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.04 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 2, t: 4, h: 1, r: 7}, 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"
}
] | 0.21 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {h: 4, k: 5, l: 6}. What is the expected number of occurrences of the pattern 'lk+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.53 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {c: 3, x: 4, z: 3} 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"
}
] | 0.4 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {r: 7, f: 2, u: 6} 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"
}
] | 0.1 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {o: 7, m: 5} to form a word, what is the expected number of matches of the pattern 'm+o'? 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 {g: 6, h: 4, v: 2, q: 1}. What is the expected number of occurrences of the pattern 'q.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.26 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {w: 6, h: 4}. What is the expected number of occurrences of the pattern 'w*h' in each word? Round your answer 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 4 letters from the multiset {h: 3, o: 3, b: 6, q: 1, l: 2}. What is the expected number of occurrences of the pattern 'lb+' in each word? Round your answer 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 5 by randomly selecting letters from the multiset {f: 2, q: 1, b: 2, i: 4, p: 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"
}
] | 0.15 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {w: 4, n: 11} to form a word, what is the expected number of matches of the pattern 'n*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.14 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {o: 4, g: 1, i: 3, a: 3, k: 2} to form a word, what is the expected number of matches of the pattern 'i*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.42 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {v: 4, s: 2, u: 2, g: 4} to form a word, what is the expected number of matches of the pattern 'u+s'? 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 5 letters from the multiset {a: 7, u: 4, k: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.31 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {r: 5, h: 7} to form a word, what is the expected number of matches of the pattern 'r+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.04 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {x: 4, g: 5, n: 3} to form a word, what is the expected number of matches of the pattern 'x*n'? 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 4 letters from the multiset {i: 4, w: 4, y: 1, g: 5}. What is the expected number of occurrences of the pattern 'iy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {s: 3, e: 1, p: 3, o: 3, n: 1} to form a word, what is the expected number of matches of the pattern 's+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.28 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {b: 1, p: 6, r: 4} to form a word, what is the expected number of matches of the pattern 'pb*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.35 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {b: 1, w: 2, a: 3, q: 1, t: 3} to form a word, what is the expected number of matches of the pattern 'qw+'? Round 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 5 by randomly selecting letters from the multiset {r: 2, i: 2, u: 6, p: 4}, what is the expected number of times the pattern 'i+r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.09 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {n: 2, e: 3, a: 4, r: 3} 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"
}
] | 0.45 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 3, r: 7}, 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"
}
] | 1.79 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {i: 2, q: 3, p: 1, h: 4} to form a word, what is the expected number of matches of the pattern 'i.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.67 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {c: 6, t: 1, z: 3, j: 3} 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"
}
] | 0.23 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {v: 8, q: 6}, what is the expected number of times the pattern 'v*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.87 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 3, m: 4, d: 5, n: 3}, 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"
}
] | 0.95 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 3, d: 4, w: 3}, 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"
}
] | 0.67 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 2, i: 2, p: 5, f: 4, z: 2}, what is the expected number of times the pattern 'p*f' 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 {c: 3, u: 5, r: 4, j: 3}, what is the expected number of times the pattern 'j*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.94 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 3, y: 9}, what is the expected number of times the pattern 't.*y' 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 {f: 1, g: 2, t: 1, k: 2, m: 4} to form a word, what is the expected number of matches of the pattern 't.*f'? 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 {z: 1, s: 2, p: 3, i: 3, l: 2}. What is the expected number of occurrences of the pattern 'i.*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.49 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 4, h: 5, k: 5}, what is the expected number of times the pattern 'kh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.94 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {p: 1, i: 3, e: 3, s: 1, d: 3} to form a word, what is the expected number of matches of the pattern 'p.*e'? 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 {x: 3, w: 3, p: 4, o: 1, j: 1}. What is the expected number of occurrences of the pattern 'pj+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.09 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {j: 7, a: 8} 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"
}
] | 2.67 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {q: 6, u: 4} to form a word, what is the expected number of matches of the pattern 'uq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.8 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {m: 3, v: 3, d: 3, x: 2, o: 3} to form a word, what is the expected number of matches of the pattern 'ov*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.3 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {j: 11, v: 3}. 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"
}
] | 3.75 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {j: 4, p: 4, g: 2, f: 4} to form a word, what is the expected number of matches of the pattern 'p*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.85 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {w: 6, b: 2, u: 4, a: 2}, what is the expected number of times the pattern 'ww+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.62 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {i: 3, f: 7, a: 5} 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"
}
] | 0.57 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {b: 2, w: 2, x: 2, g: 4}, what is the expected number of times the pattern 'w*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.09 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 7, e: 5}, what is the expected number of times the pattern 'x+e' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.76 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {e: 4, j: 3, q: 4} to form a word, what is the expected number of matches of the pattern 'q.*j'? Round 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 {u: 2, n: 4, a: 2, c: 1, b: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.09 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 5, y: 5, n: 4}, what is the expected number of times the pattern 'y.*n' 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 {g: 7, j: 6}. What is the expected number of occurrences of the pattern 'j+g' 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": "When randomly selecting 5 letters from the multiset {y: 3, g: 11} to form a word, what is the expected number of matches of the pattern 'y.*y'? 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 {t: 7, o: 2, h: 5} to form a word, what is the expected number of matches of the pattern 'oh*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {c: 3, f: 4, e: 4}, what is the expected number of times the pattern 'ef*' appears? 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 5 by randomly selecting letters from the multiset {w: 6, d: 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"
}
] | 1.82 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 3, e: 3, c: 4, i: 3}, what is the expected number of times the pattern 'c.*c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.46 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {b: 2, a: 2, v: 2, c: 1, k: 4} to form a word, what is the expected number of matches of the pattern 'kb+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.23 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {j: 3, c: 2, a: 3, q: 6} 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"
}
] | 0.07 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {h: 4, l: 4, 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"
}
] | 0.8 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 4, p: 1, x: 3, o: 2, s: 1}, what is the expected number of times the pattern 'e.*o' 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 5 by randomly selecting letters from the multiset {j: 2, r: 5, h: 1, u: 3, g: 3}, what is the expected number of times the pattern 'u+j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.15 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {d: 4, m: 3, u: 4} to form a word, what is the expected number of matches of the pattern 'du+'? 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 4 by randomly selecting letters from the multiset {a: 3, g: 3, f: 3, i: 1, n: 3}, what is the expected number of times the pattern 'f+i' 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 5 letters from the multiset {q: 6, p: 5, a: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.33 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {c: 3, x: 5, e: 3} to form a word, what is the expected number of matches of the pattern 'c.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.49 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 2, f: 1, l: 2, e: 2, c: 3}. What is the expected number of occurrences of the pattern 'cr+' in each word? Round your answer 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 {t: 4, n: 2, e: 2, z: 2, j: 3} to form a word, what is the expected number of matches of the pattern 'zt+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {v: 7, d: 3, z: 2, r: 3} to form a word, what is the expected number of matches of the pattern 'rv+'? 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 4 by randomly selecting letters from the multiset {v: 2, y: 4, b: 6}, what is the expected number of times the pattern 'yv*' appears? 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 5 by randomly selecting letters from the multiset {y: 3, b: 6, l: 2}, 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"
}
] | 2.73 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 4, f: 2, g: 1, t: 3, z: 4}, what is the expected number of times the pattern 'fk+' 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 4 letters from the multiset {e: 2, g: 4, s: 2, a: 2, n: 4}. What is the expected number of occurrences of the pattern 'g.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.26 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 5, g: 5, n: 3}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.23 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {x: 3, d: 1, e: 3, f: 2, k: 3} to form a word, what is the expected number of matches of the pattern 'k.*x'? Round 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 {v: 6, b: 3, s: 5}. What is the expected number of occurrences of the pattern 'vb+' 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": "Form a word by randomly choosing 5 letters from the multiset {s: 3, w: 3, j: 4}. What is the expected number of occurrences of the pattern 'w.*j' in each word? Round your answer 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 5 by randomly selecting letters from the multiset {j: 3, p: 3, y: 2, u: 4}, what is the expected number of times the pattern 'yu*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.14 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 7, o: 7}, what is the expected number of times the pattern 'yo+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.63 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 2, p: 4, l: 3, j: 1}, what is the expected number of times the pattern 'jl+' appears? 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 5 letters from the multiset {e: 2, a: 2, y: 2, p: 5, k: 2}. 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"
}
] | 0.11 | MATH |
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 5, k: 6, o: 4}, what is the expected number of times the pattern 'jo+' 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 5 letters from the multiset {n: 3, q: 4, z: 5} to form a word, what is the expected number of matches of the pattern 'nq+'? 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 {z: 2, s: 2, l: 4, y: 2}. What is the expected number of occurrences of the pattern 'sy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.19 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {g: 5, i: 3, x: 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"
}
] | 1.33 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {l: 2, h: 2, r: 4, w: 2}, what is the expected number of times the pattern 'wl+' 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 4 letters from the multiset {q: 3, o: 2, c: 5, x: 2} to form a word, what is the expected number of matches of the pattern 'x.*o'? Round 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 {w: 9, n: 4} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.77 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {d: 2, l: 2, k: 3, r: 3, f: 1} to form a word, what is the expected number of matches of the pattern 'l.*k'? 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 4 by randomly selecting letters from the multiset {c: 5, g: 6, o: 4}, what is the expected number of times the pattern 'oc+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.35 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {h: 4, c: 3, b: 3, a: 3, v: 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"
}
] | 0.29 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {e: 4, k: 1, z: 4, q: 3}. What is the expected number of occurrences of the pattern 'k.*k' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {o: 3, e: 3, v: 1, r: 3} to form a word, what is the expected number of matches of the pattern 'v+o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {v: 6, o: 6} to form a word, what is the expected number of matches of the pattern 'ov+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.15 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {h: 6, c: 5, i: 3} 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"
}
] | 1.1 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {b: 2, j: 6, f: 2}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.13 | MATH |
[
{
"content": "When randomly selecting 5 letters from the multiset {q: 3, g: 5, j: 2} 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"
}
] | 0.8 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {h: 5, r: 7} to form a word, what is the expected number of matches of the pattern 'hr+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.2 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {r: 2, p: 2, g: 4, i: 5}, what is the expected number of times the pattern 'i*r' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.86 | MATH |
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {u: 2, r: 4, s: 2, f: 2}. What is the expected number of occurrences of the pattern 'u+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.39 | MATH |
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