One Biased Coin

Probability Level 3

Suppose there are 1010 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 55 times. If each of the 55 flips results in heads, then the probability that this coin is fair can be written as ab\frac{a}{b}, where aa and bb are coprime positive integers. What is the value of a+ba+b?

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