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 A Game of Tennis (Posted on 2007-07-05)
When Justine serves a game of tennis against Maria, Justine wins any given point 80% of the time.
• If at some point, the game is at deuce (40-40), what is the probability Justine will eventually win?
• If it's advantage Justine ("ad in" in tennis lingo--functionally equivalent to 40-30), what are her chances?
• What is her probability of winning if the advantage is to her opponent, Maria, (equivalent to 30-40)?

Scoring in tennis is, 0, 15 (one successful point), 30 (two), 40 (three). The next point is a win unless the opponent already has 40 as well, as you must win by two points. The same player serves for the entire game, so each point within one game has the same probability given. Then the serve switches for the next game in the set or match.

• What is Justine's probability of winning the game, calculated when the score is still 0-0?
• What are the probabilities from any given state of the game?

What about when Maria is serving, if she wins any given point against Justine 75% of the time?

 See The Solution Submitted by Charlie Rating: 3.5000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: First question | Comment 2 of 6 |
(In reply to First question by Federico Kereki)

Not my strong area but here goes.
From Deuce Justine must win 2 consecutive points to win set.
Probability = 80*80/100*100=16/25
[so if Marlene is serving (9/25) since probabilities must add up to 1   - independent outcomes]
Any other combination returns through deuce and a new starting point.

 Posted by Vernon Lewis on 2007-07-05 15:19:48

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