messages listlengths 1 1 | ground_truth stringclasses 126 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "When randomly selecting 4 letters from the multiset {i: 1, y: 1, a: 2, j: 3} to form a word, what is the expected number of matches of the pattern 'j+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.28 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {a: 3, e: 1, j: 1, w: 1, y: 1}, what is the expected number of times the pattern 'yw+' 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 4 by randomly selecting letters from the multiset {i: 4, y: 2}, what is the expected number of times the pattern 'y.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.6 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 1, s: 1, i: 4, t: 2}, what is the expected number of times the pattern 'st*' 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 {q: 2, c: 3, o: 1}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {a: 3, f: 1, r: 3} to form a word, what is the expected number of matches of the pattern 'f.*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.43 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {o: 1, l: 3, v: 2} 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"
}
] | 0.23 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 2, v: 2, j: 1, q: 1, c: 1}, what is the expected number of times the pattern 'qc+' 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 3 letters from the multiset {e: 1, v: 2, o: 1, t: 3, b: 1} to form a word, what is the expected number of matches of the pattern 'vb*'? 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 {u: 2, a: 4, m: 2}. What is the expected number of occurrences of the pattern 'au+' in each word? Round your answer 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 3 letters from the multiset {m: 2, k: 3, d: 3}. What is the expected number of occurrences of the pattern 'k*m' 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": "Form a word by randomly choosing 4 letters from the multiset {z: 2, w: 4}. 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"
}
] | 2.4 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, g: 2, a: 1, d: 1}, 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"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {i: 1, y: 2, t: 1, f: 1, k: 1} 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"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {r: 1, m: 1, x: 1, e: 1, j: 4} 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"
}
] | 1.29 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, i: 1, c: 2, r: 2, d: 2}. What is the expected number of occurrences of the pattern 'm+d' 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 3 letters from the multiset {s: 1, b: 4, h: 2} to form a word, what is the expected number of matches of the pattern 'sh+'? 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 3 by randomly selecting letters from the multiset {z: 1, i: 2, q: 1, g: 2}, what is the expected number of times the pattern 'q.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {f: 4, m: 2, n: 2} to form a word, what is the expected number of matches of the pattern 'fn+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.48 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {k: 3, h: 2, p: 3} to form a word, what is the expected number of matches of the pattern 'p.*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.32 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {n: 3, h: 4} to form a word, what is the expected number of matches of the pattern 'h*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.0 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 3, x: 5}, 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"
}
] | 1.0 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {u: 5, o: 3} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.64 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {y: 2, f: 1, c: 3} 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"
}
] | 0.4 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {h: 4, p: 2, w: 1}. What is the expected number of occurrences of the pattern 'p*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.13 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {l: 2, n: 2, i: 1, t: 1, u: 2}. 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"
}
] | 0.21 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {c: 1, f: 1, w: 2, b: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'cf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.64 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, v: 1, m: 2, g: 3}, what is the expected number of times the pattern 'z.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.21 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 2, w: 1, g: 3, e: 1} to form a word, what is the expected number of matches of the pattern 'g.*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.43 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {z: 2, c: 4}, what is the expected number of times the pattern 'cz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.93 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 3, a: 4}, what is the expected number of times the pattern 'v.*v' 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 3 letters from the multiset {m: 3, z: 3, i: 2}. What is the expected number of occurrences of the pattern 'i+z' 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 {i: 2, b: 1, s: 1, y: 2, z: 1}. What is the expected number of occurrences of the pattern 'i*b' 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": "Form a word by randomly choosing 4 letters from the multiset {k: 2, a: 1, z: 3, j: 1, y: 1}. What is the expected number of occurrences of the pattern 'za*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.66 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, q: 4}, what is the expected number of times the pattern 'q.*t' 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 3 letters from the multiset {j: 3, c: 1, z: 3, q: 1} to form a word, what is the expected number of matches of the pattern 'jq+'? 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 {e: 5, b: 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"
}
] | 0.64 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, d: 2, v: 2, m: 2, z: 1}, what is the expected number of times the pattern 'd.*m' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.21 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {g: 2, o: 2, m: 2}. What is the expected number of occurrences of the pattern 'g.*m' 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": "When randomly selecting 4 letters from the multiset {v: 2, t: 1, q: 2, s: 1, n: 1} to form a word, what is the expected number of matches of the pattern 's+t'? 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 3 by randomly selecting letters from the multiset {r: 2, m: 3, h: 1}, what is the expected number of times the pattern 'r.*h' 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 {s: 2, n: 5}. What is the expected number of occurrences of the pattern 'sn*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.52 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {y: 2, r: 1, g: 1, i: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'r*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.29 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {a: 1, l: 1, x: 1, g: 3} to form a word, what is the expected number of matches of the pattern 'lx+'? 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 3 by randomly selecting letters from the multiset {u: 1, b: 1, p: 1, h: 2, a: 1}, what is the expected number of times the pattern 'hh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.13 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {h: 1, k: 1, s: 4}. What is the expected number of occurrences of the pattern 's.*k' 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 {k: 3, o: 1, f: 4}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {v: 3, c: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'v+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.56 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {t: 3, i: 1, n: 1, x: 2} 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"
}
] | 1.43 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {o: 2, y: 5}. What is the expected number of occurrences of the pattern 'yo*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.67 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, x: 2, d: 1, l: 4}. 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"
}
] | 0.64 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 2, n: 2, h: 1, i: 1, k: 1}. 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": "If you form a word of length 4 by randomly selecting letters from the multiset {m: 3, d: 3, q: 1}, what is the expected number of times the pattern 'qd+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.28 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 3, d: 1, q: 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"
}
] | 0.4 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {k: 3, n: 4}. 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"
}
] | 1.71 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {b: 2, z: 4} to form a word, what is the expected number of matches of the pattern 'z*b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.67 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {b: 3, z: 5} to form a word, what is the expected number of matches of the pattern 'b.*b'? Round 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 {w: 4, l: 3}. What is the expected number of occurrences of the pattern 'l+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.11 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, u: 1, m: 1, v: 2, j: 2}. What is the expected number of occurrences of the pattern 'i*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.48 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {y: 2, z: 1, l: 4, t: 1} to form a word, what is the expected number of matches of the pattern 'z+y'? 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 {a: 2, k: 2, w: 1, f: 1, x: 2}. What is the expected number of occurrences of the pattern 'w+x' 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 4 letters from the multiset {f: 3, j: 5}. What is the expected number of occurrences of the pattern 'f.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.61 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {u: 5, y: 2}. 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"
}
] | 1.43 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {p: 3, x: 1, r: 1, d: 1}. What is the expected number of occurrences of the pattern 'r.*r' 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 4 letters from the multiset {x: 1, f: 1, n: 2, y: 2} to form a word, what is the expected number of matches of the pattern 'xf*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.77 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {v: 1, h: 3, s: 2}. What is the expected number of occurrences of the pattern 'h*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.08 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {w: 3, u: 5} to form a word, what is the expected number of matches of the pattern 'wu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.27 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {k: 2, w: 2, r: 1, i: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'k.*k'? 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 {a: 1, d: 1, m: 2, p: 2, x: 2}. 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 4, x: 2, v: 2}, what is the expected number of times the pattern 'x+x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.07 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {k: 4, b: 4}. 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"
}
] | 2.0 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {h: 1, f: 6} to form a word, what is the expected number of matches of the pattern 'h.*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.86 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {s: 2, h: 1, e: 1, t: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'g*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.53 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {p: 1, c: 3, j: 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"
}
] | 0.43 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {a: 1, k: 6, o: 1} to form a word, what is the expected number of matches of the pattern 'ka+'? 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 {f: 2, a: 2, l: 2, n: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {w: 2, h: 2, u: 4} to form a word, what is the expected number of matches of the pattern 'u+h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.36 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, n: 2, s: 1, d: 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"
}
] | 0.32 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {f: 2, q: 1, a: 1, w: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'qa+'? 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 {i: 2, d: 1, r: 2, e: 1}. What is the expected number of occurrences of the pattern 'i+d' 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 3 letters from the multiset {e: 2, p: 1, i: 3}. What is the expected number of occurrences of the pattern 'ep*' 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": "Form a word by randomly choosing 4 letters from the multiset {q: 1, g: 1, k: 1, o: 2, s: 2}. What is the expected number of occurrences of the pattern 'k.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.29 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {r: 2, p: 3, i: 3} to form a word, what is the expected number of matches of the pattern 'r*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.36 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {a: 4, m: 4} to form a word, what is the expected number of matches of the pattern 'm+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.2 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, x: 2, w: 1, b: 1, j: 1}. What is the expected number of occurrences of the pattern 'p*b' 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": "If you form a word of length 4 by randomly selecting letters from the multiset {v: 2, o: 3, g: 1, r: 1}, what is the expected number of times the pattern 'ov*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.2 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {k: 2, p: 2, j: 1, n: 3} to form a word, what is the expected number of matches of the pattern 'p.*p'? 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 {k: 3, g: 1, m: 2, i: 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"
}
] | 0.21 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 3, h: 3, f: 1, l: 1}, what is the expected number of times the pattern 'f*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.41 | MATH |
[
{
"content": "When randomly selecting 3 letters from the multiset {u: 3, f: 2, o: 2} to form a word, what is the expected number of matches of the pattern 'f*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.07 | MATH |
[
{
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 2, i: 1, m: 2, n: 1, q: 1}, what is the expected number of times the pattern 'm.*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.29 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, w: 2, x: 1, v: 1}, what is the expected number of times the pattern 'x.*x' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 2, w: 1, r: 2, c: 2}. What is the expected number of occurrences of the pattern 'c.*c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.29 | MATH |
[
{
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 4, u: 2, q: 1}. What is the expected number of occurrences of the pattern 'r*u' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.35 | MATH |
[
{
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {n: 1, r: 1, v: 1, p: 1, x: 2}, what is the expected number of times the pattern 'rx+' 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 {g: 2, m: 1, i: 1, c: 4} to form a word, what is the expected number of matches of the pattern 'c+i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "When randomly selecting 4 letters from the multiset {k: 1, j: 4, f: 2, r: 1} to form a word, what is the expected number of matches of the pattern 'r.*f'? 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 3 by randomly selecting letters from the multiset {d: 1, f: 4, a: 2, p: 1}, what is the expected number of times the pattern 'a*d' 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 {g: 3, x: 3} 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"
}
] | 1.2 | MATH |
[
{
"content": "Form a word by randomly choosing 4 letters from the multiset {y: 1, t: 1, p: 3, r: 2}. What is the expected number of occurrences of the pattern 'tr*' 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 |
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