1995 AIME Problems/Problem 15

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Problem

Let $\displaystyle p_{}$ be the probability that, in the process of repeatedly flipping a fair coin, one will encounter a run of 5 heads before one encounters a run of 2 tails. Given that $\displaystyle p_{}$ can be written in the form $\displaystyle m/n$ where $\displaystyle m_{}$ and $\displaystyle n_{}$ are relatively prime positive integers, find $\displaystyle m+n$.

Solution

See also