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Omni-MATH / Ainsley and Buddy play a game where they repeatedly roll a standard fair…

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problem

Ainsley and Buddy play a game where they repeatedly roll a standard fair six-sided die. Ainsley wins if two multiples of 3 in a row are rolled before a non-multiple of 3 followed by a multiple of 3, and Buddy wins otherwise. If the probability that Ainsley wins is ab\frac{a}{b} for relatively prime positive integers aa and bb, compute 100a+b100a+b.
Plain-text mathematical notation (without MathML)
Ainsley and Buddy play a game where they repeatedly roll a standard fair six-sided die. Ainsley wins if two multiples of 3 in a row are rolled before a non-multiple of 3 followed by a multiple of 3, and Buddy wins otherwise. If the probability that Ainsley wins is (a)/(b) for relatively prime positive integers a and b, compute 100a+b.
Original LaTeX notation
Ainsley and Buddy play a game where they repeatedly roll a standard fair six-sided die. Ainsley wins if two multiples of 3 in a row are rolled before a non-multiple of 3 followed by a multiple of 3, and Buddy wins otherwise. If the probability that Ainsley wins is $\frac{a}{b}$ for relatively prime positive integers $a$ and $b$, compute $100a+b$.

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Source and history

task_id
caf7ca94-18f9-5d0a-89e9-3e56868908e9
task_key
test--caf7ca94-18f9-5d0a-89e9-3e56868908e9
task_revision_id
1
config / split
/ test

Official source

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