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Omni-MATH / A jar contains 8 red balls and 2 blue balls. Every minute, a ball is randomly…

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problem

A jar contains 8 red balls and 2 blue balls. Every minute, a ball is randomly removed. The probability that there exists a time during this process where there are more blue balls than red balls in the jar can be expressed as ab\frac{a}{b} for relatively prime integers aa and bb. Compute 100a+b100 a+b.
Plain-text mathematical notation (without MathML)
A jar contains 8 red balls and 2 blue balls. Every minute, a ball is randomly removed. The probability that there exists a time during this process where there are more blue balls than red balls in the jar can be expressed as (a)/(b) for relatively prime integers a and b. Compute 100a+b.
Original LaTeX notation
A jar contains 8 red balls and 2 blue balls. Every minute, a ball is randomly removed. The probability that there exists a time during this process where there are more blue balls than red balls in the jar can be expressed as $\frac{a}{b}$ for relatively prime integers $a$ and $b$. Compute $100 a+b$.

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Source and history

task_id
25d88a3a-7fa7-5817-acfe-2ff49a0ab007
task_key
test--25d88a3a-7fa7-5817-acfe-2ff49a0ab007
task_revision_id
1
config / split
/ test

Official source

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