Tennis Probability
Combinatorics · problem by Abdallah Y.
Two players are playing in a tennis match, and are at deuce (that is, they will play back and forth until one person has scored two more points than the other). The first player has a 60% chance of winning every point, and the second player has a 40% chance of winning every point. What is the probability that the first player wins the match?
The answer is in the form $\frac{\alpha}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.