# Infinite Rolling of Coins

Discrete Mathematics Level 4

Let $$p$$ 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 $$p$$ can be written in the form $$\frac{m}{n},$$ where $$m$$ and $$n$$ are relatively prime positive integers, find $$m + n.$$

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