messages
listlengths 1
1
| ground_truth
stringclasses 13
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {j: 1, u: 1, i: 1, o: 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 {w: 2, a: 2}. What is the expected number of occurrences of the pattern 'a*w' 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 2 by randomly selecting letters from the multiset {b: 1, t: 1, j: 1, f: 1}, 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"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 2 letters from the multiset {l: 3, z: 1} to form a word, what is the expected number of matches of the pattern 'l+z'? 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 {f: 1, b: 3} 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"
}
] |
0.5
|
MATH
|
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {m: 1, w: 1, g: 1, o: 1}, 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"
}
] |
0.08
|
MATH
|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {w: 2, b: 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"
}
] |
0.17
|
MATH
|
[
{
"content": "When randomly selecting 2 letters from the multiset {h: 3, n: 1} 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"
}
] |
0.75
|
MATH
|
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {l: 1, f: 1, o: 2}, what is the expected number of times the pattern 'o+l' 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 {v: 1, b: 2, g: 1}, 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 3, u: 1}, what is the expected number of times the pattern 'q+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 {i: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'i+m'? Round 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 {c: 2, s: 1, b: 1} to form a word, what is the expected number of matches of the pattern 'sc+'? 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 {z: 2, r: 2}, what is the expected number of times the pattern 'zr+' 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 {h: 1, j: 1, l: 1, g: 1}, what is the expected number of times the pattern 'gh+' 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 {k: 2, c: 2} to form a word, what is the expected number of matches of the pattern 'kc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.33
|
MATH
|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {v: 1, s: 2, n: 1}. What is the expected number of occurrences of the pattern 'v+n' 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 {f: 1, j: 3} to form a word, what is the expected number of matches of the pattern 'j+f'? 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: 3}. What is the expected number of occurrences of the pattern 'io*' 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": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 2, j: 1, q: 1}, 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"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {u: 1, h: 2, f: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 2 letters from the multiset {r: 1, n: 1, z: 1, w: 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": "If you form a word of length 2 by randomly selecting letters from the multiset {g: 1, j: 1, y: 1, r: 1}, what is the expected number of times the pattern 'y*g' 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 {z: 1, w: 3} to form a word, what is the expected number of matches of the pattern 'zw*'? 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 {r: 1, n: 1, p: 1, e: 1}, what is the expected number of times the pattern 'p+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.08
|
MATH
|
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 1, y: 1, z: 1, h: 1}, what is the expected number of times the pattern 'yz+' 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, u: 1, s: 1, j: 1}, what is the expected number of times the pattern 'js*' appears? 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 {s: 1, a: 2, 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": "If you form a word of length 2 by randomly selecting letters from the multiset {p: 1, x: 1, m: 2}, what is the expected number of times the pattern 'm.*x' 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 {a: 1, m: 3}. What is the expected number of occurrences of the pattern 'am+' 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": "Form a word by randomly choosing 2 letters from the multiset {a: 1, l: 1, r: 1, n: 1}. What is the expected number of occurrences of the pattern 'ln+' 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 {s: 2, n: 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 {l: 2, r: 2}, what is the expected number of times the pattern 'r+l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.33
|
MATH
|
[
{
"content": "When randomly selecting 2 letters from the multiset {o: 1, h: 1, b: 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"
}
] |
0.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {g: 1, i: 3}. What is the expected number of occurrences of the pattern 'i+g' 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": "Form a word by randomly choosing 2 letters from the multiset {f: 1, n: 1, p: 1, w: 1}. What is the expected number of occurrences of the pattern 'n.*w' 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 {q: 1, s: 1, r: 1, z: 1}, what is the expected number of times the pattern 'sz+' 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, x: 1, z: 1, a: 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"
}
] |
0.58
|
MATH
|
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {r: 2, w: 2}, what is the expected number of times the pattern 'wr*' appears? 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 2 by randomly selecting letters from the multiset {b: 1, f: 1, y: 1, t: 1}, 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"
}
] |
0.58
|
MATH
|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {e: 1, x: 2, v: 1}. What is the expected number of occurrences of the pattern 'x.*x' 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 {l: 2, p: 1, f: 1}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 2, x: 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"
}
] |
0.17
|
MATH
|
[
{
"content": "When randomly selecting 2 letters from the multiset {m: 3, t: 1} to form a word, what is the expected number of matches of the pattern 'm*t'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.75
|
MATH
|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {n: 1, q: 1, f: 1, i: 1}. What is the expected number of occurrences of the pattern 'n+f' 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 {z: 2, r: 2}. What is the expected number of occurrences of the pattern 'r+z' 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 {r: 1, x: 2, y: 1} to form a word, what is the expected number of matches of the pattern 'y+r'? 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 {g: 1, x: 1, p: 1, h: 1}, what is the expected number of times the pattern 'gh+' 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 {j: 3, i: 1}, what is the expected number of times the pattern 'i.*i' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {o: 1, z: 1, a: 1, i: 1}. What is the expected number of occurrences of the pattern 'a+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": "When randomly selecting 2 letters from the multiset {b: 1, s: 1, n: 1, g: 1} to form a word, what is the expected number of matches of the pattern 's.*g'? 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 {e: 1, x: 1, q: 1, z: 1}. What is the expected number of occurrences of the pattern 'e.*q' 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 {z: 1, j: 1, n: 2}. What is the expected number of occurrences of the pattern 'n*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": "If you form a word of length 2 by randomly selecting letters from the multiset {b: 2, w: 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 {i: 1, p: 1, o: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {b: 2, c: 2}. What is the expected number of occurrences of the pattern 'c+b' 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": "If you form a word of length 2 by randomly selecting letters from the multiset {k: 1, p: 1, q: 1, x: 1}, what is the expected number of times the pattern 'k.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {m: 1, f: 2, d: 1}. What is the expected number of occurrences of the pattern 'd.*m' 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 {k: 1, j: 1, e: 1, o: 1}. What is the expected number of occurrences of the pattern 'je*' 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": "Form a word by randomly choosing 2 letters from the multiset {v: 1, o: 1, l: 1, m: 1}. What is the expected number of occurrences of the pattern 'o+v' 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 {e: 2, h: 2} to form a word, what is the expected number of matches of the pattern 'h+e'? Round 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 {j: 2, m: 2} to form a word, what is the expected number of matches of the pattern 'm.*m'? 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 {x: 2, v: 2}, what is the expected number of times the pattern 'v*x' appears? 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 2 by randomly selecting letters from the multiset {l: 1, x: 1, c: 1, k: 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 2 letters from the multiset {d: 1, s: 3}. What is the expected number of occurrences of the pattern 'd+s' 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 {t: 1, l: 1, n: 2} to form a word, what is the expected number of matches of the pattern 'n.*l'? 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 {e: 1, l: 3} to form a word, what is the expected number of matches of the pattern 'e.*e'? 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 {b: 1, f: 2, i: 1}. 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"
}
] |
0.17
|
MATH
|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {k: 1, f: 3}. What is the expected number of occurrences of the pattern 'f.*f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
MATH
|
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 3, u: 1}, what is the expected number of times the pattern 'nu+' 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 {j: 1, e: 3} to form a word, what is the expected number of matches of the pattern 'e.*e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
MATH
|
[
{
"content": "When randomly selecting 2 letters from the multiset {v: 2, f: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'g.*f'? 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 {y: 3, s: 1}. What is the expected number of occurrences of the pattern 's.*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
MATH
|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {k: 2, v: 2}. What is the expected number of occurrences of the pattern 'k+v' 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": "If you form a word of length 2 by randomly selecting letters from the multiset {k: 1, b: 1, n: 1, p: 1}, 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"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 2 letters from the multiset {h: 1, o: 2, t: 1} 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": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 1, u: 1, z: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {x: 1, f: 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"
}
] |
0.0
|
MATH
|
[
{
"content": "When randomly selecting 2 letters from the multiset {o: 3, b: 1} to form a word, what is the expected number of matches of the pattern 'ob*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.75
|
MATH
|
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 3, v: 1}, what is the expected number of times the pattern 'hv*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.75
|
MATH
|
[
{
"content": "When randomly selecting 2 letters from the multiset {a: 1, o: 1, m: 1, y: 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": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 2, d: 1, t: 1}, what is the expected number of times the pattern 't+d' 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 {g: 1, h: 1, m: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'gx*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.58
|
MATH
|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {r: 2, t: 2}. What is the expected number of occurrences of the pattern 'r+t' 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 {k: 2, z: 2} 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"
}
] |
0.17
|
MATH
|
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 2, y: 2}, 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"
}
] |
0.17
|
MATH
|
[
{
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 1, p: 1, a: 1, o: 1}, 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"
}
] |
0.58
|
MATH
|
[
{
"content": "When randomly selecting 2 letters from the multiset {y: 1, v: 1, l: 2} to form a word, what is the expected number of matches of the pattern 'vl*'? 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 {r: 3, d: 1}, what is the expected number of times the pattern 'r*d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.75
|
MATH
|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {m: 1, j: 2, s: 1}. What is the expected number of occurrences of the pattern 's.*m' 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 {g: 3, x: 1}. What is the expected number of occurrences of the pattern 'g.*x' 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": "Form a word by randomly choosing 2 letters from the multiset {o: 1, e: 1, v: 2}. What is the expected number of occurrences of the pattern 'o+e' 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 {o: 2, u: 2} to form a word, what is the expected number of matches of the pattern 'u*o'? 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 {t: 1, m: 1, a: 1, g: 1}. What is the expected number of occurrences of the pattern 'ma+' 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 {b: 2, p: 1, n: 1}. What is the expected number of occurrences of the pattern 'p*p' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
MATH
|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {l: 1, o: 1, j: 1, h: 1}. What is the expected number of occurrences of the pattern 'h+o' 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 {n: 1, h: 1, s: 1, k: 1} 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"
}
] |
0.08
|
MATH
|
[
{
"content": "Form a word by randomly choosing 2 letters from the multiset {u: 1, y: 2, c: 1}. What is the expected number of occurrences of the pattern 'uc*' 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": "If you form a word of length 2 by randomly selecting letters from the multiset {u: 1, g: 1, k: 2}, what is the expected number of times the pattern 'u+g' 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 {p: 1, z: 1, j: 1, t: 1}. What is the expected number of occurrences of the pattern 'p.*p' 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
|
End of preview. Expand
in Data Studio
No dataset card yet
- Downloads last month
- 7