In a grueling Wimbledon final the scoreline is tied at \(2\) sets all. In the final set, Djokovic who is leading the set \(7-6\), is serving for game set and match. After six points, scores are level at \(40-40\) Deuce.
Having the serve, Djokovic has a \(0.75\) chance of winning a point against Federer while a tiring Federer has a \(0.25\) chance of winning a point against Djokovic.
What is the probability that Djokovic wins this game after Deuce is reached?
Details and assumptions
- To win the game, Djokovic can win the first \(2\) points.
- If he wins the first point and loses the second, its back to Deuce
- If he loses the first point and wins the second, its back to Deuce.
- If he loses the first \(2\) points he loses the game.