A Coin Flipping Game

Discrete Mathematics Level 3

You and your friend play a game where you take turns flipping a fair coin. If it's tails, the other player gets to take a turn; if it's heads, the current player wins and the game is over.

If you go first, what is the probability that you will win?

If this probability can be expressed as \( \frac ab\), where \( a\) and \(b\) are coprime positive integers, enter your answer as \(a + b\).

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