A man has to win two games in a row in order to win a prize. In total, he has to play only three games. The opponents are weak or strong. He has to at least play one strong opponent, and he cannot play consecutively two weak opponents. What sequence should he choose to play?
(In reply to
Too simple by Old Original Oskar!)
For example, consider a case where the probability of winning a game against a strong player is 1/4 and against a weak player is 3/4.
The probability of winning the prize is the probability of winning the middle game times the probability of winning either or both of the other two games. This latter is 1 minus the probability of losing both the first and last games.
So when middle game is against the strong player, the probability of winning the prize is 1/4 * (1  (1/4)^2) = 15/64; when the middle game is against the weak player, the probability of winning the prize is 3/4 * (1  (3/4)^2) = 21/64.

Posted by Charlie
on 20060801 09:12:17 