[User]
Form a word by randomly choosing 5 letters from the multiset {p: 3, a: 8}. What is the expected number of occurrences of the pattern 'a.*a' in each word? Round your answer to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}

dataset: MATH


[User]
If you form a word of length 5 by randomly selecting letters from the multiset {x: 2, n: 4, u: 3, d: 3}, what is the expected number of times the pattern 'x+u' appears? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Form a word by randomly choosing 5 letters from the multiset {u: 5, c: 1, a: 1, p: 3}. What is the expected number of occurrences of the pattern 'ac+' in each word? Round your answer to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Form a word by randomly choosing 5 letters from the multiset {m: 3, u: 7}. What is the expected number of occurrences of the pattern 'm.*m' in each word? Round your answer to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Form a word by randomly choosing 5 letters from the multiset {i: 2, n: 3, r: 4, c: 2}. What is the expected number of occurrences of the pattern 'c*i' in each word? Round your answer to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Form a word by randomly choosing 5 letters from the multiset {c: 2, d: 5, v: 3}. What is the expected number of occurrences of the pattern 'dv+' in each word? Round your answer to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Form a word by randomly choosing 5 letters from the multiset {x: 6, n: 6}. What is the expected number of occurrences of the pattern 'n.*x' in each word? Round your answer to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
If you form a word of length 5 by randomly selecting letters from the multiset {x: 2, y: 1, a: 4, s: 2}, what is the expected number of times the pattern 'yx*' appears? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
If you form a word of length 5 by randomly selecting letters from the multiset {u: 4, f: 2, l: 5}, what is the expected number of times the pattern 'l*f' appears? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
If you form a word of length 5 by randomly selecting letters from the multiset {p: 4, s: 1, w: 3, o: 4}, what is the expected number of times the pattern 'o*s' appears? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Form a word by randomly choosing 5 letters from the multiset {f: 2, y: 2, v: 4, o: 2}. What is the expected number of occurrences of the pattern 'y.*o' in each word? Round your answer to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Form a word by randomly choosing 5 letters from the multiset {i: 2, m: 4, g: 2, y: 3}. What is the expected number of occurrences of the pattern 'y.*y' in each word? Round your answer to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
If you form a word of length 5 by randomly selecting letters from the multiset {o: 1, a: 2, b: 3, z: 2, w: 2}, what is the expected number of times the pattern 'w.*w' appears? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {u: 5, n: 2, c: 5} to form a word, what is the expected number of matches of the pattern 'uc*'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
If you form a word of length 5 by randomly selecting letters from the multiset {u: 2, k: 2, x: 3, r: 1, z: 2}, what is the expected number of times the pattern 'r.*x' appears? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
If you form a word of length 5 by randomly selecting letters from the multiset {f: 5, o: 7}, what is the expected number of times the pattern 'f.*f' appears? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
If you form a word of length 5 by randomly selecting letters from the multiset {z: 4, e: 2, b: 2, x: 3}, what is the expected number of times the pattern 'e*b' appears? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Form a word by randomly choosing 5 letters from the multiset {w: 7, a: 2}. What is the expected number of occurrences of the pattern 'w.*w' in each word? Round your answer to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
If you form a word of length 5 by randomly selecting letters from the multiset {h: 4, r: 3, v: 3, e: 2}, what is the expected number of times the pattern 'r.*r' appears? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {o: 1, l: 2, m: 7, t: 1} to form a word, what is the expected number of matches of the pattern 't*m'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {c: 2, a: 2, t: 3, i: 1, e: 2} to form a word, what is the expected number of matches of the pattern 't*a'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Form a word by randomly choosing 5 letters from the multiset {k: 1, f: 3, e: 3, a: 5}. What is the expected number of occurrences of the pattern 'e.*e' in each word? Round your answer to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Form a word by randomly choosing 5 letters from the multiset {a: 5, t: 5}. What is the expected number of occurrences of the pattern 'a+t' in each word? Round your answer to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
If you form a word of length 5 by randomly selecting letters from the multiset {m: 3, v: 3, f: 6}, what is the expected number of times the pattern 'mv*' appears? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
If you form a word of length 5 by randomly selecting letters from the multiset {o: 3, c: 3, u: 4}, what is the expected number of times the pattern 'o*u' appears? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {e: 3, q: 1, z: 5} to form a word, what is the expected number of matches of the pattern 'e.*q'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {c: 2, i: 2, l: 2, g: 4, f: 2} to form a word, what is the expected number of matches of the pattern 'c.*i'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
If you form a word of length 5 by randomly selecting letters from the multiset {n: 5, w: 7}, what is the expected number of times the pattern 'n.*n' appears? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
If you form a word of length 5 by randomly selecting letters from the multiset {g: 1, k: 4, v: 1, b: 3, q: 2}, what is the expected number of times the pattern 'g+k' appears? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {f: 1, q: 5, n: 3} to form a word, what is the expected number of matches of the pattern 'q.*n'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Form a word by randomly choosing 5 letters from the multiset {t: 2, u: 3, v: 2, x: 3}. What is the expected number of occurrences of the pattern 'u*t' in each word? Round your answer to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {g: 3, x: 1, l: 5, j: 1, t: 1} to form a word, what is the expected number of matches of the pattern 'jt+'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {f: 3, k: 4, q: 2} to form a word, what is the expected number of matches of the pattern 'f.*f'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {t: 6, y: 3} to form a word, what is the expected number of matches of the pattern 't+y'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {w: 4, d: 8} to form a word, what is the expected number of matches of the pattern 'wd+'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
If you form a word of length 5 by randomly selecting letters from the multiset {u: 2, k: 3, i: 2, o: 3}, what is the expected number of times the pattern 'o.*o' appears? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {q: 1, a: 4, y: 5} to form a word, what is the expected number of matches of the pattern 'y.*y'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Form a word by randomly choosing 5 letters from the multiset {b: 1, g: 4, h: 2, f: 3, k: 1}. What is the expected number of occurrences of the pattern 'kg*' in each word? Round your answer to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Form a word by randomly choosing 5 letters from the multiset {k: 3, w: 4, q: 3}. What is the expected number of occurrences of the pattern 'qw*' in each word? Round your answer to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {o: 3, q: 5, t: 2, b: 2} to form a word, what is the expected number of matches of the pattern 'q+t'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {d: 6, f: 4} to form a word, what is the expected number of matches of the pattern 'df*'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Form a word by randomly choosing 5 letters from the multiset {h: 4, n: 6, a: 2}. What is the expected number of occurrences of the pattern 'h.*h' in each word? Round your answer to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {o: 7, e: 4} to form a word, what is the expected number of matches of the pattern 'o*e'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Form a word by randomly choosing 5 letters from the multiset {o: 4, j: 3, p: 2, u: 3}. What is the expected number of occurrences of the pattern 'o+j' in each word? Round your answer to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {u: 3, i: 2, k: 2, q: 2, d: 2} to form a word, what is the expected number of matches of the pattern 'iu*'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Form a word by randomly choosing 5 letters from the multiset {g: 2, l: 3, e: 1, j: 3, d: 1}. What is the expected number of occurrences of the pattern 'e.*l' in each word? Round your answer to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {p: 2, o: 5, i: 2} to form a word, what is the expected number of matches of the pattern 'po*'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {g: 3, b: 6, d: 1} to form a word, what is the expected number of matches of the pattern 'd.*d'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
When randomly selecting 5 letters from the multiset {l: 2, b: 3, n: 1, h: 4} to form a word, what is the expected number of matches of the pattern 'n.*n'? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}


[User]
If you form a word of length 5 by randomly selecting letters from the multiset {h: 3, a: 2, p: 2, i: 3, y: 2}, what is the expected number of times the pattern 'i+a' appears? Round to 2 decimal places.

Present the answer in LaTex format: \boxed{Your answer}