messages
listlengths 1
1
| ground_truth
stringclasses 85
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {t: 2, r: 3, e: 4, v: 1}. What is the expected number of occurrences of the pattern 'te*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.48
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {z: 4, v: 3, k: 1, m: 2}. What is the expected number of occurrences of the pattern 'v*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.64
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 7, y: 3}, what is the expected number of times the pattern 'a+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.79
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {a: 1, e: 1, q: 2, i: 3, j: 3}. 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"
}
] |
0.16
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {n: 2, f: 2, x: 5, y: 1}, 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"
}
] |
0.19
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {y: 2, d: 2, n: 6}. What is the expected number of occurrences of the pattern 'y*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.19
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {l: 4, e: 4, g: 2}. What is the expected number of occurrences of the pattern 'e+l' 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": "When randomly selecting 5 letters from the multiset {q: 6, u: 2, y: 2} 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"
}
] |
3.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {g: 3, q: 2, h: 1, r: 2, k: 2}. What is the expected number of occurrences of the pattern 'kh*' 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": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 5, a: 5}, what is the expected number of times the pattern 't.*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.22
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {w: 1, x: 3, t: 6} to form a word, what is the expected number of matches of the pattern 'tw+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.27
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {n: 2, q: 2, f: 1, d: 3, x: 2} 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 6, f: 4}, what is the expected number of times the pattern 'fl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.8
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {b: 1, a: 2, s: 3, o: 4}. What is the expected number of occurrences of the pattern 'a*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.39
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {l: 4, q: 3, d: 3}. What is the expected number of occurrences of the pattern 'dq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.98
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {u: 1, n: 5, b: 1, q: 1, l: 2}, 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"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {a: 1, b: 1, w: 4, y: 1, o: 3} to form a word, what is the expected number of matches of the pattern 'wo+'? 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 5 letters from the multiset {x: 1, i: 1, o: 4, s: 1, t: 3}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {q: 2, v: 2, e: 2, w: 3, i: 1}. What is the expected number of occurrences of the pattern 'wq*' in each word? Round your answer 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 {v: 2, z: 1, y: 4, t: 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"
}
] |
1.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 1, q: 3, n: 2, y: 2, u: 2}. What is the expected number of occurrences of the pattern 'u*q' in each word? Round your answer 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 {x: 6, k: 4} to form a word, what is the expected number of matches of the pattern 'kx+'? 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 {u: 2, g: 2, v: 4, r: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'uv*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.48
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {c: 1, a: 5, b: 4} to form a word, what is the expected number of matches of the pattern 'c*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.72
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {p: 3, v: 7}. What is the expected number of occurrences of the pattern 'vp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.62
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {h: 7, q: 3}, what is the expected number of times the pattern 'h*q' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.29
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {o: 1, b: 4, w: 3, n: 2} 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"
}
] |
1.33
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {m: 4, x: 3, j: 3}, what is the expected number of times the pattern 'mx+' appears? 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 5 by randomly selecting letters from the multiset {l: 2, n: 2, z: 3, g: 3}, what is the expected number of times the pattern 'nl*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.19
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {o: 3, v: 2, m: 3, l: 2} to form a word, what is the expected number of matches of the pattern 'v.*v'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {k: 3, z: 2, x: 2, r: 1, p: 2}, what is the expected number of times the pattern 'pk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.32
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 2, m: 1, q: 3, n: 2, p: 2}. What is the expected number of occurrences of the pattern 'dq+' 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": "When randomly selecting 5 letters from the multiset {x: 2, l: 3, o: 3, m: 2} 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"
}
] |
1.79
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {w: 2, a: 2, e: 1, p: 4, k: 1} to form a word, what is the expected number of matches of the pattern 'w*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.39
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {e: 4, o: 3, d: 3}, what is the expected number of times the pattern 'e+d' appears? 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 5 letters from the multiset {c: 3, t: 2, g: 4, e: 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"
}
] |
0.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {z: 2, w: 2, g: 2, f: 1, e: 3}, what is the expected number of times the pattern 'g*f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {f: 2, d: 4, n: 4} 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": "When randomly selecting 5 letters from the multiset {f: 5, s: 3, o: 2} to form a word, what is the expected number of matches of the pattern 'fo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.99
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 3, m: 2, u: 1, t: 2, i: 2} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 2, k: 3, q: 2, c: 3}, 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"
}
] |
0.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {g: 3, m: 3, s: 4}, what is the expected number of times the pattern 'gm+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.48
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {k: 2, e: 3, s: 1, t: 3, i: 1} to form a word, what is the expected number of matches of the pattern 'i.*e'? Round 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 {w: 3, v: 7}. What is the expected number of occurrences of the pattern 'vw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.62
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {m: 7, g: 3} to form a word, what is the expected number of matches of the pattern 'm+g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.79
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {l: 3, d: 3, z: 4}. What is the expected number of occurrences of the pattern 'lz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.21
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {m: 3, z: 3, i: 3, v: 1}, what is the expected number of times the pattern 'iv+' 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 5 by randomly selecting letters from the multiset {a: 5, j: 5}, what is the expected number of times the pattern 'aj+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {j: 4, r: 4, g: 2}, what is the expected number of times the pattern 'jg+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.39
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {w: 2, k: 3, x: 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"
}
] |
1.33
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {x: 6, c: 4}, what is the expected number of times the pattern 'x+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.8
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {a: 5, w: 2, g: 3}, what is the expected number of times the pattern 'w.*g' 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 {j: 2, i: 3, b: 1, h: 4} 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"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {l: 1, i: 2, o: 2, q: 3, n: 2} to form a word, what is the expected number of matches of the pattern 'iq*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.32
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {m: 3, c: 2, b: 2, w: 3} to form a word, what is the expected number of matches of the pattern 'ww*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.79
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {y: 6, r: 4}, 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"
}
] |
1.33
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {r: 5, a: 5} to form a word, what is the expected number of matches of the pattern 'ra+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {y: 2, r: 2, n: 3, j: 3} to form a word, what is the expected number of matches of the pattern 'j.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {s: 3, q: 3, f: 2, i: 2}. What is the expected number of occurrences of the pattern 'i*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.79
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {p: 1, e: 2, l: 1, z: 6}. What is the expected number of occurrences of the pattern 'p.*l' 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 {g: 1, x: 4, b: 2, u: 3}, 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"
}
] |
1.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {d: 3, s: 3, i: 2, f: 2}. What is the expected number of occurrences of the pattern 'i*s' in each word? Round your answer 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 {k: 4, h: 4, j: 2} to form a word, what is the expected number of matches of the pattern 'j*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.39
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {q: 7, p: 3}. What is the expected number of occurrences of the pattern 'qp+' 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 5 letters from the multiset {f: 3, u: 2, b: 2, i: 1, k: 2}. What is the expected number of occurrences of the pattern 'f+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 5 by randomly selecting letters from the multiset {j: 4, d: 2, u: 4}, 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"
}
] |
0.48
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {p: 3, j: 4, f: 3}. What is the expected number of occurrences of the pattern 'p*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.98
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {w: 3, l: 2, v: 1, c: 2, q: 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"
}
] |
0.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {t: 2, g: 3, s: 5}, what is the expected number of times the pattern 'gs+' appears? 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 5 by randomly selecting letters from the multiset {u: 5, q: 5}, what is the expected number of times the pattern 'uq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.17
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {i: 2, p: 4, a: 4}, what is the expected number of times the pattern 'ai*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.39
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {g: 3, w: 4, q: 3}, what is the expected number of times the pattern 'w+g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.71
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {m: 6, y: 4} to form a word, what is the expected number of matches of the pattern 'y+m'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.43
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {k: 3, c: 2, x: 4, f: 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"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {i: 2, w: 2, j: 1, p: 4, o: 1} to form a word, what is the expected number of matches of the pattern 'w+p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.39
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {j: 3, l: 3, s: 4}. 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"
}
] |
0.67
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {c: 7, p: 3}. What is the expected number of occurrences of the pattern 'cp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.63
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {l: 3, r: 4, s: 3}. 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"
}
] |
0.67
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {o: 5, b: 5} 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"
}
] |
2.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 3, q: 2, o: 3, x: 1, e: 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": "When randomly selecting 5 letters from the multiset {q: 3, p: 7} to form a word, what is the expected number of matches of the pattern 'p.*q'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {l: 4, o: 1, a: 5}. What is the expected number of occurrences of the pattern 'l*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.69
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {r: 3, p: 2, h: 5} to form a word, what is the expected number of matches of the pattern 'p.*r'? 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 {q: 8, y: 2}, what is the expected number of times the pattern 'q+y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.56
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {b: 3, h: 5, z: 2}. 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"
}
] |
1.09
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {b: 2, z: 4, n: 2, y: 2}. 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"
}
] |
0.22
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {o: 4, c: 3, r: 3}, what is the expected number of times the pattern 'cr*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.98
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {c: 2, q: 3, u: 5}. What is the expected number of occurrences of the pattern 'c*q' in each word? Round your answer 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 {k: 3, u: 2, t: 3, n: 2} to form a word, what is the expected number of matches of the pattern 't+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.48
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {t: 1, l: 1, v: 2, r: 4, n: 2} to form a word, what is the expected number of matches of the pattern 'v+r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.39
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {q: 4, p: 1, x: 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"
}
] |
0.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 5, a: 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"
}
] |
1.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {l: 1, z: 1, x: 2, w: 4, g: 2}, what is the expected number of times the pattern 'g.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.22
|
MATH
|
[
{
"content": "Form a word by randomly choosing 5 letters from the multiset {m: 3, f: 7}. 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"
}
] |
4.67
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {c: 2, h: 1, t: 2, p: 1, o: 4}, what is the expected number of times the pattern 'pt+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
MATH
|
[
{
"content": "When randomly selecting 5 letters from the multiset {y: 1, b: 3, n: 2, x: 2, z: 2} to form a word, what is the expected number of matches of the pattern 'nz*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.19
|
MATH
|
[
{
"content": "If you form a word of length 5 by randomly selecting letters from the multiset {r: 6, p: 4}, what is the expected number of times the pattern 'p.*r' appears? Round 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 5 letters from the multiset {h: 4, x: 6}. What is the expected number of occurrences of the pattern 'x.*h' 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 5 letters from the multiset {i: 4, x: 2, o: 1, b: 2, a: 1}. 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 5 by randomly selecting letters from the multiset {b: 1, x: 1, q: 6, o: 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"
}
] |
0.0
|
MATH
|
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