id stringlengths 39 39 | setting_key stringclasses 1
value | setting_name stringclasses 0
values | messages listlengths 1 1 | ground_truth stringclasses 126
values | dataset stringclasses 1
value |
|---|---|---|---|---|---|
combinatory_pattern_matching_train_0200 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 1, h: 3, s: 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0201 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 2, m: 3, n: 1}, what is the expected number of times the pattern 'm+n' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.25 | math |
combinatory_pattern_matching_train_0202 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 1, q: 1, t: 1, j: 1}, what is the expected number of times the pattern 'hq+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.08 | math |
combinatory_pattern_matching_train_0203 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 2, p: 1, r: 1, f: 2}, 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}"
}
] | 0.07 | math |
combinatory_pattern_matching_train_0204 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, h: 1, m: 1, n: 1}. What is the expected number of occurrences of the pattern 'm.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.25 | math |
combinatory_pattern_matching_train_0205 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, h: 1, a: 2}. What is the expected number of occurrences of the pattern 'h+f' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.17 | math |
combinatory_pattern_matching_train_0206 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {t: 1, w: 1, j: 2, z: 2}. What is the expected number of occurrences of the pattern 'j.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.4 | math |
combinatory_pattern_matching_train_0207 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {c: 3, z: 2, k: 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}"
}
] | 0.6 | math |
combinatory_pattern_matching_train_0208 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 2, y: 2, x: 2}, what is the expected number of times the pattern 'fx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.3 | math |
combinatory_pattern_matching_train_0209 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {s: 4, r: 2} to form a word, what is the expected number of matches of the pattern 'rs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.93 | math |
combinatory_pattern_matching_train_0210 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, x: 4}, what is the expected number of times the pattern 'x.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.6 | math |
combinatory_pattern_matching_train_0211 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {l: 3, y: 2} 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}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0212 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {r: 3, h: 1}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0213 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {l: 1, u: 2, y: 1, p: 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}"
}
] | 0.3 | math |
combinatory_pattern_matching_train_0214 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {x: 1, f: 3} to form a word, what is the expected number of matches of the pattern 'fx+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.5 | math |
combinatory_pattern_matching_train_0215 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {w: 4, q: 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}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0216 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {e: 2, a: 2}. What is the expected number of occurrences of the pattern 'ae+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.33 | math |
combinatory_pattern_matching_train_0217 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {d: 1, e: 2, i: 1} 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}"
}
] | 0.17 | math |
combinatory_pattern_matching_train_0218 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, m: 1, n: 1, t: 2, h: 1}. What is the expected number of occurrences of the pattern 'ht*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.65 | math |
combinatory_pattern_matching_train_0219 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {p: 2, h: 3}. What is the expected number of occurrences of the pattern 'ph+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.8 | math |
combinatory_pattern_matching_train_0220 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {c: 3, y: 2}. What is the expected number of occurrences of the pattern 'yc*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.1 | math |
combinatory_pattern_matching_train_0221 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {g: 2, p: 3}, what is the expected number of times the pattern 'p*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.0 | math |
combinatory_pattern_matching_train_0222 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {j: 2, p: 4}. What is the expected number of occurrences of the pattern 'p+j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.73 | math |
combinatory_pattern_matching_train_0223 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {j: 2, t: 1, e: 2, x: 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}"
}
] | 0.8 | math |
combinatory_pattern_matching_train_0224 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {k: 3, b: 1}, what is the expected number of times the pattern 'kk*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.0 | math |
combinatory_pattern_matching_train_0225 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {v: 1, u: 1, f: 2, b: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'v+b'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.03 | math |
combinatory_pattern_matching_train_0226 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {h: 2, c: 2, f: 1}, what is the expected number of times the pattern 'c.*h' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0227 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {c: 2, j: 1, i: 1, l: 1}. What is the expected number of occurrences of the pattern 'li+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.05 | math |
combinatory_pattern_matching_train_0228 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {e: 1, r: 1, o: 1, i: 1, v: 2} to form a word, what is the expected number of matches of the pattern 'i.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0229 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, w: 1, j: 2}, what is the expected number of times the pattern 'w.*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.25 | math |
combinatory_pattern_matching_train_0230 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 2, y: 1, i: 1, n: 1, v: 1}, what is the expected number of times the pattern 'y.*v' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0231 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 1, x: 2, a: 1, n: 1, z: 1}, what is the expected number of times the pattern 'xz+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.07 | math |
combinatory_pattern_matching_train_0232 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 2, c: 1, t: 1, d: 1, b: 1}, what is the expected number of times the pattern 'cd*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.57 | math |
combinatory_pattern_matching_train_0233 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 2, x: 3}, what is the expected number of times the pattern 'xf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.3 | math |
combinatory_pattern_matching_train_0234 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {v: 2, p: 1, d: 1, u: 1, f: 1} to form a word, what is the expected number of matches of the pattern 'dv+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.07 | math |
combinatory_pattern_matching_train_0235 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {t: 1, z: 2, s: 1, k: 1}, what is the expected number of times the pattern 'ks+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0236 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {y: 4, l: 2}, what is the expected number of times the pattern 'ly*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.93 | math |
combinatory_pattern_matching_train_0237 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {x: 1, e: 1, n: 2, y: 1, h: 1}. 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}"
}
] | 0.57 | math |
combinatory_pattern_matching_train_0238 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {d: 3, k: 2}, what is the expected number of times the pattern 'k+d' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.3 | math |
combinatory_pattern_matching_train_0239 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 2, r: 2, f: 1, z: 1}, what is the expected number of times the pattern 'zh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.65 | math |
combinatory_pattern_matching_train_0240 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {l: 3, m: 1, w: 1}. What is the expected number of occurrences of the pattern 'l.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.15 | math |
combinatory_pattern_matching_train_0241 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {o: 1, x: 1, h: 1, w: 1}, what is the expected number of times the pattern 'wx*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.92 | math |
combinatory_pattern_matching_train_0242 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, u: 1, e: 1}, 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}"
}
] | 0.9 | math |
combinatory_pattern_matching_train_0243 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {v: 1, a: 2, w: 1, c: 2} to form a word, what is the expected number of matches of the pattern 'v*a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.13 | math |
combinatory_pattern_matching_train_0244 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {c: 1, e: 1, p: 1, b: 1, r: 1}, 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}"
}
] | 0.05 | math |
combinatory_pattern_matching_train_0245 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {f: 1, z: 1, w: 1, n: 1, g: 1} to form a word, what is the expected number of matches of the pattern 'f.*n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.05 | math |
combinatory_pattern_matching_train_0246 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {q: 1, k: 3}, what is the expected number of times the pattern 'q.*k' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.25 | math |
combinatory_pattern_matching_train_0247 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {c: 1, s: 2, w: 1}. What is the expected number of occurrences of the pattern 'c*s' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.17 | math |
combinatory_pattern_matching_train_0248 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {v: 2, q: 2, h: 2}, what is the expected number of times the pattern 'qh*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.3 | math |
combinatory_pattern_matching_train_0249 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {h: 3, z: 3}. 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}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0250 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {t: 3, c: 1} to form a word, what is the expected number of matches of the pattern 't*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.75 | math |
combinatory_pattern_matching_train_0251 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {g: 1, f: 1, n: 1, q: 1} to form a word, what is the expected number of matches of the pattern 'q*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.92 | math |
combinatory_pattern_matching_train_0252 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 1, i: 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0253 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {a: 2, g: 2, z: 1, i: 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}"
}
] | 0.07 | math |
combinatory_pattern_matching_train_0254 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {h: 2, w: 4} to form a word, what is the expected number of matches of the pattern 'w.*w'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.2 | math |
combinatory_pattern_matching_train_0255 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {x: 1, d: 1, h: 2} to form a word, what is the expected number of matches of the pattern 'd.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.08 | math |
combinatory_pattern_matching_train_0256 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {p: 4, o: 1}, what is the expected number of times the pattern 'o+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.4 | math |
combinatory_pattern_matching_train_0257 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {d: 1, r: 2, y: 2}. What is the expected number of occurrences of the pattern 'd*y' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.9 | math |
combinatory_pattern_matching_train_0258 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {o: 3, n: 1}. What is the expected number of occurrences of the pattern 'no*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.5 | math |
combinatory_pattern_matching_train_0259 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {l: 3, f: 3}. What is the expected number of occurrences of the pattern 'fl*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.3 | math |
combinatory_pattern_matching_train_0260 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {n: 3, x: 3} to form a word, what is the expected number of matches of the pattern 'xn*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.25 | math |
combinatory_pattern_matching_train_0261 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {a: 1, m: 3, p: 1} 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}"
}
] | 0.9 | math |
combinatory_pattern_matching_train_0262 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {x: 3, c: 1, l: 2}, what is the expected number of times the pattern 'l+c' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.15 | math |
combinatory_pattern_matching_train_0263 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {a: 2, g: 1, e: 1, i: 1, t: 1} to form a word, what is the expected number of matches of the pattern 't*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.37 | math |
combinatory_pattern_matching_train_0264 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 1, y: 1, d: 2, f: 1}. What is the expected number of occurrences of the pattern 'd.*r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.3 | math |
combinatory_pattern_matching_train_0265 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {p: 2, z: 1, h: 1, c: 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}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0266 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {k: 2, r: 1, l: 1, i: 2} to form a word, what is the expected number of matches of the pattern 'il+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.13 | math |
combinatory_pattern_matching_train_0267 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {c: 1, z: 1, o: 1, n: 1, p: 2}. What is the expected number of occurrences of the pattern 'n+c' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.07 | math |
combinatory_pattern_matching_train_0268 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {v: 1, k: 1, y: 1, j: 1, s: 1}, what is the expected number of times the pattern 'vk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.05 | math |
combinatory_pattern_matching_train_0269 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {d: 2, c: 1, h: 1, z: 2}. What is the expected number of occurrences of the pattern 'hz*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.4 | math |
combinatory_pattern_matching_train_0270 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {j: 3, e: 3}. What is the expected number of occurrences of the pattern 'e.*j' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.3 | math |
combinatory_pattern_matching_train_0271 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 3, z: 1, m: 1}, 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0272 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {a: 2, b: 3}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0273 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {q: 1, i: 2, d: 3} 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}"
}
] | 0.6 | math |
combinatory_pattern_matching_train_0274 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {p: 2, z: 1, y: 1, u: 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}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0275 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {q: 1, n: 1, d: 1, p: 1, r: 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0276 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {r: 1, l: 1, m: 1, t: 1}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0277 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {n: 2, b: 1, l: 1, c: 1} 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0278 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, c: 1, h: 1, g: 1, f: 1}, 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0279 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {y: 2, e: 2, l: 2} to form a word, what is the expected number of matches of the pattern 'y+e'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.3 | math |
combinatory_pattern_matching_train_0280 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {r: 2, f: 1, i: 2, o: 1} 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0281 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {q: 1, j: 1, h: 1, t: 1, y: 1}, what is the expected number of times the pattern 'yq*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.7 | math |
combinatory_pattern_matching_train_0282 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {s: 2, r: 3}. 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}"
}
] | 0.3 | math |
combinatory_pattern_matching_train_0283 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {o: 1, f: 2, u: 3}, what is the expected number of times the pattern 'f.*u' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0284 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {n: 1, h: 1, o: 1, s: 2, z: 1}, what is the expected number of times the pattern 'z*o' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.37 | math |
combinatory_pattern_matching_train_0285 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {p: 1, z: 1, q: 2, k: 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}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0286 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {m: 1, k: 1, d: 2}. What is the expected number of occurrences of the pattern 'd.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.5 | math |
combinatory_pattern_matching_train_0287 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {d: 1, s: 4}. What is the expected number of occurrences of the pattern 's.*d' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0288 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 2 letters from the multiset {r: 2, c: 2, k: 1} to form a word, what is the expected number of matches of the pattern 'k+c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0289 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {f: 2, t: 1, j: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0290 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {l: 2, g: 1, y: 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}"
}
] | 0.07 | math |
combinatory_pattern_matching_train_0291 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 2 letters from the multiset {l: 1, n: 2, e: 1}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0292 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {n: 2, b: 1, j: 1, l: 1}. 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0293 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {b: 1, c: 4}, 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0294 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, r: 2}. What is the expected number of occurrences of the pattern 'rd*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.0 | math |
combinatory_pattern_matching_train_0295 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 2, b: 3}. What is the expected number of occurrences of the pattern 'rr*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.4 | math |
combinatory_pattern_matching_train_0296 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {l: 2, z: 1, x: 2}, what is the expected number of times the pattern 'x.*z' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.3 | math |
combinatory_pattern_matching_train_0297 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 2, q: 1, d: 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0298 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {w: 1, y: 1, h: 1, q: 1}. What is the expected number of occurrences of the pattern 'y+w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.17 | math |
combinatory_pattern_matching_train_0299 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 2 by randomly selecting letters from the multiset {w: 1, c: 1, a: 1, s: 2, j: 1}, what is the expected number of times the pattern 'j.*j' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
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