Recursion: Tennis 2

In a tennis match between Federer and Nadal, the score starts at 30 - 30. Federer has a 60% chance of winning each serve, independent of previous serves. What is the probability that Federer wins the game from this point?

Answer

Let \(P_1\) be the probability that Federer wins from 30-30, and \(P_2\) be the probability that he wins from deuce.

This sets up the recursion:

\[ P_1 = 0.36 + 0.48 \times P_2. \]

But \(P_1\) and \(P_2\) is the same since they both require two consecutive wins to win. Hence the answer is the same as in "Recursion: Tennis 1", which is \(9/13\).

Notes and comments

Comment 1: Even if we did not make the connection about \(P_1\) and \(P_2\) we would still have the same result.

Back to collection