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 $a + b$ .