Tossing the Coin

Wayne and Mario play a game in which they take turns flipping a fair coin. The first one to flip tails win. Wayne goes first. What is the probability that Wayne wins?

The answer will be of form \(\frac{A}{B}\) where \(A\) are \(B\) are positive co-prime integers. Find \(A+B+A \times B\).


Note: this problem is taken from AoPS
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