Roger Federer is serving for the Australian Open and it is deuce. This means tha

Question

Roger Federer is serving for the Australian Open and it is deuce. This means that the score is tied and a player wins the game if he is two points ahead of the other player. The probability that Federer gets his first serve in is 0.6. If his first serve is a fault he gets his second serve in with probability 1. The probability that he wins a point on his first serve is 0.9, and that he wins a point on his second serve is 0.6. Suppose this is true independently for all points, what is the probability that Federer wins the game?

Explanation / Answer

Solution:

P (first serve) = 0.6, P (1st serve fault|won second) = 1,

P (wins point and first serve) = 0.9

P (wins point and second serve) = 0.6

Therefore, the probability of win is

P (win) = P (first serve)*P (wins point and first serve) +P (fault)*P (wins point and second serve)

P (win) =0.6*0.9 + (1 - 0.6)*0.6

P (win) = 0.78

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