messages listlengths 1 1 | ground_truth stringclasses 13
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {b: 2, p: 2}, what is the expected number of times the pattern 'p.*p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {b: 1, y: 1, t: 1, l: 1} to form a word, what is the expected number of matches of the pattern 'tt+'? 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 2 letters from the multiset {v: 2, n: 2}. What is the expected number of occurrences of the pattern 'vn+' 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 2 letters from the multiset {b: 1, x: 2, d: 1} to form a word, what is the expected number of matches of the pattern 'dd*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {i: 1, k: 2, g: 1}, what is the expected number of times the pattern 'g.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {j: 2, h: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'h.*h'? 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 2 letters from the multiset {c: 2, j: 1, e: 1}. 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {p: 2, q: 1, n: 1} 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {u: 1, z: 1, d: 2}. What is the expected number of occurrences of the pattern 'du*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {p: 2, e: 2} 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"
}
] | 0.33 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 1, a: 1, m: 2}, what is the expected number of times the pattern 'fa*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {d: 1, n: 3} to form a word, what is the expected number of matches of the pattern 'd+n'? Round 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 2 by randomly selecting letters from the multiset {k: 1, v: 1, s: 2}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {u: 2, m: 2}. What is the expected number of occurrences of the pattern 'm*u' 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": "When randomly selecting 2 letters from the multiset {v: 1, j: 1, z: 2} to form a word, what is the expected number of matches of the pattern 'vj+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 2, g: 2}, what is the expected number of times the pattern 'm*g' 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 2 letters from the multiset {b: 1, w: 1, u: 1, e: 1}. 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {n: 2, q: 1, w: 1}. What is the expected number of occurrences of the pattern 'nq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {s: 3, m: 1} to form a word, what is the expected number of matches of the pattern 'm*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.75 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {z: 1, x: 1, r: 1, c: 1}. What is the expected number of occurrences of the pattern 'z.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {b: 2, r: 1, g: 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {k: 1, m: 1, c: 1, e: 1} to form a word, what is the expected number of matches of the pattern 'e+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 2, m: 1, f: 1}, what is the expected number of times the pattern 'mn*' 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 2 letters from the multiset {r: 1, m: 1, h: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'h.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {x: 1, o: 2, i: 1} to form a word, what is the expected number of matches of the pattern 'oi*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {m: 2, g: 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"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 1, x: 3}, what is the expected number of times the pattern 's+x' appears? Round 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 2 by randomly selecting letters from the multiset {l: 2, f: 1, k: 1}, what is the expected number of times the pattern 'l+f' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {k: 1, h: 1, z: 1, w: 1}. What is the expected number of occurrences of the pattern 'h+z' 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": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 1, v: 2, l: 1}, what is the expected number of times the pattern 'wv*' 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 2 by randomly selecting letters from the multiset {d: 3, f: 1}, what is the expected number of times the pattern 'f.*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {f: 1, c: 2, z: 1}. What is the expected number of occurrences of the pattern 'f.*c' 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": "Form a word by randomly choosing 2 letters from the multiset {d: 2, h: 2}. What is the expected number of occurrences of the pattern 'h+d' 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 2 letters from the multiset {e: 1, h: 1, r: 2} 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"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 1, k: 2, n: 1}, what is the expected number of times the pattern 'ns+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {a: 1, u: 2, o: 1}, 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {j: 2, u: 2}, 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"
}
] | 0.33 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {s: 2, r: 2}, what is the expected number of times the pattern 's.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {p: 1, v: 1, s: 1, r: 1}. What is the expected number of occurrences of the pattern 'r+p' 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 2 letters from the multiset {n: 2, p: 2}. What is the expected number of occurrences of the pattern 'np*' 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": "Form a word by randomly choosing 2 letters from the multiset {s: 3, j: 1}. 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 2, w: 1, n: 1}, what is the expected number of times the pattern 'n.*w' appears? Round 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 2 letters from the multiset {f: 2, b: 1, g: 1}. 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {v: 1, e: 1, l: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'l*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 3, d: 1}, what is the expected number of times the pattern 'g*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.75 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {t: 3, p: 1}, what is the expected number of times the pattern 'p*t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.75 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {x: 2, g: 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"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 3, c: 1}, what is the expected number of times the pattern 'c+w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {v: 1, k: 1, p: 1, n: 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 2, t: 1, l: 1}, what is the expected number of times the pattern 't*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {j: 1, a: 1, k: 1, r: 1} to form a word, what is the expected number of matches of the pattern 'rk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 2, o: 2}, what is the expected number of times the pattern 'ow*' 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 2 letters from the multiset {g: 1, k: 1, s: 2} to form a word, what is the expected number of matches of the pattern 'g+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {n: 1, b: 3} to form a word, what is the expected number of matches of the pattern 'n+b'? Round 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 2 by randomly selecting letters from the multiset {a: 2, r: 2}, what is the expected number of times the pattern 'ra*' 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 2 letters from the multiset {g: 1, l: 1, o: 1, w: 1} to form a word, what is the expected number of matches of the pattern 'lo*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 2, a: 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"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {f: 1, c: 2, a: 1} 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"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {n: 1, d: 2, l: 1} to form a word, what is the expected number of matches of the pattern 'l.*l'? 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 2 by randomly selecting letters from the multiset {r: 1, g: 3}, what is the expected number of times the pattern 'r.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {i: 1, o: 1, z: 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"
}
] | 1.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {n: 2, r: 2} 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"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {k: 3, h: 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"
}
] | 0.5 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 1, l: 1, u: 2}, what is the expected number of times the pattern 'um*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {i: 2, h: 1, d: 1} to form a word, what is the expected number of matches of the pattern 'hi*'? 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 2 by randomly selecting letters from the multiset {e: 1, y: 1, l: 1, p: 1}, what is the expected number of times the pattern 'p.*p' 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 2 by randomly selecting letters from the multiset {o: 3, u: 1}, what is the expected number of times the pattern 'o.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {l: 1, a: 2, y: 1} 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"
}
] | 1.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 1, z: 1, n: 1, e: 1}, what is the expected number of times the pattern 'nc+' appears? Round 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 2 letters from the multiset {s: 1, t: 1, e: 1, g: 1}. 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 3, y: 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {k: 1, p: 1, o: 2}. What is the expected number of occurrences of the pattern 'k*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 1, a: 1, m: 1, r: 1}, what is the expected number of times the pattern 'm.*a' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {z: 1, t: 1, e: 1, n: 1}, what is the expected number of times the pattern 'n+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.08 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 1, w: 1, h: 2}, what is the expected number of times the pattern 'ho+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.17 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {s: 1, k: 1, y: 1, b: 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {k: 1, v: 3}. What is the expected number of occurrences of the pattern 'kv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.75 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {r: 1, k: 1, u: 1, d: 1} 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {y: 2, c: 2}. What is the expected number of occurrences of the pattern 'y.*c' 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 2 letters from the multiset {c: 1, v: 1, w: 1, e: 1}. What is the expected number of occurrences of the pattern 've+' 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": "When randomly selecting 2 letters from the multiset {p: 1, j: 1, h: 1, a: 1} 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"
}
] | 0.0 | MATH |
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {i: 1, w: 1, r: 1, d: 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"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {v: 2, w: 2} to form a word, what is the expected number of matches of the pattern 'vw*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {f: 1, q: 1, z: 1, o: 1} to form a word, what is the expected number of matches of the pattern 'z*f'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {z: 2, w: 2}, what is the expected number of times the pattern 'wz*' 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 2 letters from the multiset {z: 2, b: 2}. What is the expected number of occurrences of the pattern 'z*b' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {d: 1, f: 2, c: 1} to form a word, what is the expected number of matches of the pattern 'd*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {z: 1, q: 1, t: 1, x: 1}, what is the expected number of times the pattern 'z.*z' 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 2 by randomly selecting letters from the multiset {p: 1, g: 2, d: 1}, what is the expected number of times the pattern 'g*p' 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 2 by randomly selecting letters from the multiset {w: 1, m: 2, l: 1}, what is the expected number of times the pattern 'm*w' appears? 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 2 letters from the multiset {w: 3, n: 1}. What is the expected number of occurrences of the pattern 'w+n' 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": "When randomly selecting 2 letters from the multiset {d: 2, b: 1, p: 1} to form a word, what is the expected number of matches of the pattern 'pp+'? 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 2 letters from the multiset {o: 2, c: 1, r: 1}. What is the expected number of occurrences of the pattern 'c.*o' 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": "When randomly selecting 2 letters from the multiset {w: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'wk*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.33 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {u: 1, k: 1, o: 2} 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"
}
] | 0.0 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 2, y: 2}, 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"
}
] | 0.17 | MATH |
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {e: 2, z: 2}, 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"
}
] | 1.33 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {t: 1, f: 3} to form a word, what is the expected number of matches of the pattern 't.*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {r: 1, z: 1, i: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'zi*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.58 | MATH |
[
{
"content": "When randomly selecting 2 letters from the multiset {u: 3, k: 1} to form a word, what is the expected number of matches of the pattern 'u+k'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.25 | MATH |
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