2008 Mock ARML 1 Problems/Problem 4

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Problem

There are $4$ black balls and $1$ white ball in a hat. A turn consists of picking a ball from the hat and replacing it with one of the opposite color. Compute the probability that, after a sequence of turns, there are $5$ black balls in the hat before there are $5$ white balls.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it. The answer is $\boxed{\frac{5}{8}}$.

See also

2008 Mock ARML 1 (Problems, Source)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5 6 7 8