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_0900 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {k: 3, z: 4}. What is the expected number of occurrences of the pattern 'kz+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.74 | math |
combinatory_pattern_matching_train_0901 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {o: 1, e: 1, a: 1, y: 3, p: 2}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0902 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {o: 1, c: 2, h: 1, n: 1, s: 1} to form a word, what is the expected number of matches of the pattern 's.*s'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0903 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {o: 3, j: 3} to form a word, what is the expected number of matches of the pattern 'j.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.6 | math |
combinatory_pattern_matching_train_0904 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 1, w: 1, y: 1, o: 2, c: 1}, what is the expected number of times the pattern 'u.*y' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0905 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {d: 3, h: 2, n: 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}"
}
] | 0.86 | math |
combinatory_pattern_matching_train_0906 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {v: 1, h: 2, f: 3} to form a word, what is the expected number of matches of the pattern 'f*h'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.17 | math |
combinatory_pattern_matching_train_0907 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {s: 2, g: 2, v: 4} to form a word, what is the expected number of matches of the pattern 'v*g'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.6 | math |
combinatory_pattern_matching_train_0908 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {g: 1, r: 4, j: 3} to form a word, what is the expected number of matches of the pattern 'rj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.0 | math |
combinatory_pattern_matching_train_0909 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {d: 1, n: 1, c: 2, o: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'cc*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.11 | math |
combinatory_pattern_matching_train_0910 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {m: 3, z: 4, v: 1}, what is the expected number of times the pattern 'mz*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.66 | math |
combinatory_pattern_matching_train_0911 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {f: 1, w: 1, k: 3, j: 1}. What is the expected number of occurrences of the pattern 'fk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.08 | math |
combinatory_pattern_matching_train_0912 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 4, x: 2}, what is the expected number of times the pattern 'x+t' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.93 | math |
combinatory_pattern_matching_train_0913 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {a: 2, d: 2, k: 2} to form a word, what is the expected number of matches of the pattern 'k+a'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.47 | math |
combinatory_pattern_matching_train_0914 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 1, m: 1, t: 1, i: 2, g: 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0915 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 2, s: 1, o: 2, c: 1, e: 1}, what is the expected number of times the pattern 'e*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.48 | math |
combinatory_pattern_matching_train_0916 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 4, w: 1, e: 1, s: 2}, what is the expected number of times the pattern 'sh+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.36 | math |
combinatory_pattern_matching_train_0917 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {y: 2, v: 1, g: 4}, what is the expected number of times the pattern 'g.*g' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.86 | math |
combinatory_pattern_matching_train_0918 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {k: 4, w: 2}. What is the expected number of occurrences of the pattern 'wk*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.67 | math |
combinatory_pattern_matching_train_0919 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {n: 1, l: 1, z: 2, i: 3} to form a word, what is the expected number of matches of the pattern 'l+n'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.07 | math |
combinatory_pattern_matching_train_0920 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {r: 3, t: 1, o: 3, q: 1} to form a word, what is the expected number of matches of the pattern 't.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.32 | math |
combinatory_pattern_matching_train_0921 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {u: 2, t: 1, c: 1, n: 1, i: 2}, 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0922 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {x: 1, a: 1, u: 2, c: 2}. What is the expected number of occurrences of the pattern 'x.*a' 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_0923 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {a: 2, l: 1, x: 2, i: 1, v: 1} to form a word, what is the expected number of matches of the pattern 'i.*x'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.29 | math |
combinatory_pattern_matching_train_0924 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {x: 3, p: 3}. What is the expected number of occurrences of the pattern 'xp*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.25 | math |
combinatory_pattern_matching_train_0925 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {a: 4, j: 3} to form a word, what is the expected number of matches of the pattern 'aj*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.4 | math |
combinatory_pattern_matching_train_0926 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {r: 3, n: 1, b: 4}, what is the expected number of times the pattern 'nb*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.55 | math |
combinatory_pattern_matching_train_0927 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {f: 1, d: 3, e: 3, n: 1} to form a word, what is the expected number of matches of the pattern 'ed*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.1 | math |
combinatory_pattern_matching_train_0928 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {a: 3, h: 2, e: 1, z: 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}"
}
] | 0.73 | math |
combinatory_pattern_matching_train_0929 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {e: 2, z: 1, f: 2, s: 1, j: 2}, what is the expected number of times the pattern 'e*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.62 | math |
combinatory_pattern_matching_train_0930 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {r: 1, o: 1, f: 3, e: 2} to form a word, what is the expected number of matches of the pattern 'e*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.53 | math |
combinatory_pattern_matching_train_0931 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {c: 2, b: 2, y: 2}. What is the expected number of occurrences of the pattern 'cy+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.47 | math |
combinatory_pattern_matching_train_0932 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, b: 1, z: 3, n: 1}. What is the expected number of occurrences of the pattern 'z*n' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.75 | math |
combinatory_pattern_matching_train_0933 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, l: 3, o: 1, 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}"
}
] | 0.1 | math |
combinatory_pattern_matching_train_0934 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {s: 1, i: 1, z: 2, a: 3, k: 1}. What is the expected number of occurrences of the pattern 'k.*z' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.21 | math |
combinatory_pattern_matching_train_0935 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {i: 1, j: 2, h: 2, a: 1} to form a word, what is the expected number of matches of the pattern 'i.*j'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.4 | math |
combinatory_pattern_matching_train_0936 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {f: 1, r: 1, j: 1, c: 2, p: 1}. What is the expected number of occurrences of the pattern 'c+r' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.23 | math |
combinatory_pattern_matching_train_0937 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {q: 4, g: 3}. What is the expected number of occurrences of the pattern 'g*q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3.4 | math |
combinatory_pattern_matching_train_0938 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {i: 3, b: 3, v: 1} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.86 | math |
combinatory_pattern_matching_train_0939 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {c: 5, k: 1, g: 2} to form a word, what is the expected number of matches of the pattern 'c.*c'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.07 | math |
combinatory_pattern_matching_train_0940 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {i: 1, e: 1, a: 1, h: 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0941 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {h: 1, l: 1, g: 3, a: 1, d: 2}, what is the expected number of times the pattern 'ha*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.41 | math |
combinatory_pattern_matching_train_0942 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 1, r: 3, f: 3}, what is the expected number of times the pattern 'sr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.17 | math |
combinatory_pattern_matching_train_0943 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {o: 2, e: 1, w: 4}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.71 | math |
combinatory_pattern_matching_train_0944 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {c: 2, p: 2, t: 3, u: 1}. What is the expected number of occurrences of the pattern 't.*t' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.32 | math |
combinatory_pattern_matching_train_0945 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {i: 1, v: 2, q: 2, r: 3}. What is the expected number of occurrences of the pattern 'ri*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.23 | math |
combinatory_pattern_matching_train_0946 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {d: 2, m: 1, w: 2, s: 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}"
}
] | 0.08 | math |
combinatory_pattern_matching_train_0947 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {p: 2, o: 2, h: 1, y: 2}. What is the expected number of occurrences of the pattern 'ho+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.16 | math |
combinatory_pattern_matching_train_0948 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {d: 1, n: 1, s: 1, r: 1, l: 2}, what is the expected number of times the pattern 'l*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.9 | math |
combinatory_pattern_matching_train_0949 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {g: 4, c: 4} to form a word, what is the expected number of matches of the pattern 'cg*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3.2 | math |
combinatory_pattern_matching_train_0950 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {n: 1, y: 1, i: 2, f: 2}, what is the expected number of times the pattern 'fi*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.8 | math |
combinatory_pattern_matching_train_0951 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {x: 2, i: 2, v: 2, a: 2}, what is the expected number of times the pattern 'ia*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.24 | math |
combinatory_pattern_matching_train_0952 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {g: 2, t: 4} 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}"
}
] | 2.4 | math |
combinatory_pattern_matching_train_0953 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {a: 7, o: 1} to form a word, what is the expected number of matches of the pattern 'oa*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.25 | math |
combinatory_pattern_matching_train_0954 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {i: 1, r: 2, m: 1, o: 1, j: 1} to form a word, what is the expected number of matches of the pattern 'ji*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.57 | math |
combinatory_pattern_matching_train_0955 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {b: 2, z: 5} 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}"
}
] | 1.24 | math |
combinatory_pattern_matching_train_0956 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {k: 1, s: 3, r: 1, y: 1}, what is the expected number of times the pattern 'kr+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.07 | math |
combinatory_pattern_matching_train_0957 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {b: 3, z: 1, t: 3, l: 1}, what is the expected number of times the pattern 'tl+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.11 | math |
combinatory_pattern_matching_train_0958 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {f: 4, j: 2}. 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}"
}
] | 2.4 | math |
combinatory_pattern_matching_train_0959 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {d: 2, t: 1, h: 2, e: 2, v: 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0960 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {w: 5, i: 1}, what is the expected number of times the pattern 'i*w' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.83 | math |
combinatory_pattern_matching_train_0961 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {w: 1, f: 3, r: 4} to form a word, what is the expected number of matches of the pattern 'f.*r'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.29 | math |
combinatory_pattern_matching_train_0962 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {m: 4, w: 3}. What is the expected number of occurrences of the pattern 'mw*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.4 | math |
combinatory_pattern_matching_train_0963 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {z: 3, p: 1, i: 4}, what is the expected number of times the pattern 'i+p' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.18 | math |
combinatory_pattern_matching_train_0964 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {y: 2, w: 3, o: 2} 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}"
}
] | 0.29 | math |
combinatory_pattern_matching_train_0965 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, o: 1, x: 2}. What is the expected number of occurrences of the pattern 'd*o' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.75 | math |
combinatory_pattern_matching_train_0966 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {i: 2, v: 5} to form a word, what is the expected number of matches of the pattern 'i.*i'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.14 | math |
combinatory_pattern_matching_train_0967 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {y: 1, c: 4, s: 3} to form a word, what is the expected number of matches of the pattern 'cs*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.0 | math |
combinatory_pattern_matching_train_0968 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {v: 3, x: 5}. What is the expected number of occurrences of the pattern 'x*v' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.77 | math |
combinatory_pattern_matching_train_0969 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {s: 4, o: 3} to form a word, what is the expected number of matches of the pattern 'o.*o'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.43 | math |
combinatory_pattern_matching_train_0970 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {p: 1, w: 2, l: 1, u: 1, x: 1} to form a word, what is the expected number of matches of the pattern 'xu+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.07 | math |
combinatory_pattern_matching_train_0971 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {s: 2, t: 2, l: 2}, what is the expected number of times the pattern 'l.*l' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0972 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {s: 2, q: 4, n: 1} to form a word, what is the expected number of matches of the pattern 'sq+'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.5 | math |
combinatory_pattern_matching_train_0973 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {o: 3, p: 1, i: 2, s: 1} to form a word, what is the expected number of matches of the pattern 'o*p'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.85 | math |
combinatory_pattern_matching_train_0974 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {y: 2, a: 1, q: 1, m: 2} to form a word, what is the expected number of matches of the pattern 'a+y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.13 | math |
combinatory_pattern_matching_train_0975 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {f: 4, d: 2}. What is the expected number of occurrences of the pattern 'fd+' 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_0976 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {z: 2, x: 2, i: 1, l: 1, o: 1}. What is the expected number of occurrences of the pattern 'zx+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.21 | math |
combinatory_pattern_matching_train_0977 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 4, e: 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}"
}
] | 1.71 | math |
combinatory_pattern_matching_train_0978 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {f: 3, l: 1, z: 1, t: 2, s: 1}, what is the expected number of times the pattern 'f*s' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.5 | math |
combinatory_pattern_matching_train_0979 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {t: 4, r: 4}, 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}"
}
] | 1.29 | math |
combinatory_pattern_matching_train_0980 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {q: 1, e: 1, v: 1, y: 2, m: 2}, what is the expected number of times the pattern 'qy+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.16 | math |
combinatory_pattern_matching_train_0981 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {g: 2, n: 2, i: 3, f: 1}, what is the expected number of times the pattern 'ni*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.4 | math |
combinatory_pattern_matching_train_0982 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {n: 1, x: 2, i: 1, v: 1, y: 1} to form a word, what is the expected number of matches of the pattern 'x.*y'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | math |
combinatory_pattern_matching_train_0983 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {o: 3, m: 3} to form a word, what is the expected number of matches of the pattern 'om*'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.25 | math |
combinatory_pattern_matching_train_0984 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {j: 4, f: 1, k: 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}"
}
] | 2.4 | math |
combinatory_pattern_matching_train_0985 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {f: 1, n: 5, c: 2}. 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}"
}
] | 0.24 | math |
combinatory_pattern_matching_train_0986 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 3 letters from the multiset {k: 2, d: 4} to form a word, what is the expected number of matches of the pattern 'k*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.6 | math |
combinatory_pattern_matching_train_0987 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {l: 6, v: 2}. What is the expected number of occurrences of the pattern 'lv*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.71 | math |
combinatory_pattern_matching_train_0988 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {z: 1, n: 2, e: 2, f: 2}. What is the expected number of occurrences of the pattern 'nf+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.32 | math |
combinatory_pattern_matching_train_0989 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 3 by randomly selecting letters from the multiset {a: 1, w: 2, l: 1, h: 1, e: 1}, what is the expected number of times the pattern 'el*' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.57 | math |
combinatory_pattern_matching_train_0990 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {y: 1, f: 2, b: 2, k: 1, a: 1}. What is the expected number of occurrences of the pattern 'y+k' 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_0991 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {f: 3, n: 1, i: 1, l: 1}, what is the expected number of times the pattern 'lf+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.42 | math |
combinatory_pattern_matching_train_0992 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {u: 4, g: 4} to form a word, what is the expected number of matches of the pattern 'u.*u'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.29 | math |
combinatory_pattern_matching_train_0993 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {r: 2, a: 1, k: 1, q: 1, b: 1}. What is the expected number of occurrences of the pattern 'q+q' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0994 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {j: 1, t: 1, y: 2, b: 2}. 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}"
}
] | 0.0 | math |
combinatory_pattern_matching_train_0995 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {r: 3, n: 2, o: 1, v: 1}. What is the expected number of occurrences of the pattern 'vr+' 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_0996 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "When randomly selecting 4 letters from the multiset {p: 2, l: 3, d: 2} to form a word, what is the expected number of matches of the pattern 'p*d'? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.47 | math |
combinatory_pattern_matching_train_0997 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "If you form a word of length 4 by randomly selecting letters from the multiset {p: 2, r: 1, k: 2, n: 1}, what is the expected number of times the pattern 'rk+' appears? Round to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.23 | math |
combinatory_pattern_matching_train_0998 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 4 letters from the multiset {i: 4, z: 2, s: 1, j: 1}. What is the expected number of occurrences of the pattern 'is+' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.21 | math |
combinatory_pattern_matching_train_0999 | combinatory_pattern_matching | null | [
{
"role": "user",
"content": "Form a word by randomly choosing 3 letters from the multiset {d: 3, q: 3}. What is the expected number of occurrences of the pattern 'dq*' in each word? Round your answer to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.25 | math |
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