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?

(In reply to re: First question by Vernon Lewis)

This must be wrong, since if we take it the other way, you get a different result.

If Maria is to win, she must get two consecutive points, so the probability would be 0.2x0.2=1/25 and Justine's should be 24/25.

If the same reasoning applied the other way round produces different results, it must be wrong.

Calculating the odds that Justine wins, GIVEN THAT SOMEONE WINS, makes her probability 16/17, and Maria's 1/17.

Posted by Old Original Oskar! on 2007-07-05 22:33:35