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Omni-MATH / Roger initially has 20 socks in a drawer, each of which is either white or…

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problem

Roger initially has 20 socks in a drawer, each of which is either white or black. He chooses a sock uniformly at random from the drawer and throws it away. He repeats this action until there are equal numbers of white and black socks remaining. Suppose that the probability he stops before all socks are gone is pp. If the sum of all distinct possible values of pp over all initial combinations of socks is ab\frac{a}{b} for relatively prime positive integers aa and bb, compute 100a+b100 a+b
Plain-text mathematical notation (without MathML)
Roger initially has 20 socks in a drawer, each of which is either white or black. He chooses a sock uniformly at random from the drawer and throws it away. He repeats this action until there are equal numbers of white and black socks remaining. Suppose that the probability he stops before all socks are gone is p. If the sum of all distinct possible values of p over all initial combinations of socks is (a)/(b) for relatively prime positive integers a and b, compute 100a+b
Original LaTeX notation
Roger initially has 20 socks in a drawer, each of which is either white or black. He chooses a sock uniformly at random from the drawer and throws it away. He repeats this action until there are equal numbers of white and black socks remaining. Suppose that the probability he stops before all socks are gone is $p$. If the sum of all distinct possible values of $p$ over all initial combinations of socks is $\frac{a}{b}$ for relatively prime positive integers $a$ and $b$, compute $100 a+b$

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Source and history

task_id
ee744076-9553-5b03-a3e7-633764910f46
task_key
test--ee744076-9553-5b03-a3e7-633764910f46
task_revision_id
1
config / split
/ test

Official source

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