# One Biased Coin

Suppose there are $$10$$ coins laid out in front of you. All of the coins are fair (i.e. have an equal chance of heads or tails) except one, which flips to heads every time. You draw one coin at random and flip it $$5$$ times. If each of the $$5$$ flips results in heads, then the probability that this coin is fair can be written as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a+b$$?

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