Tennis,anyone? (Posted on 2010-09-07)

	Submitted by Ady TZIDON
Rating: 5.0000 (1 votes)
Solution:	(Hide)
Charlie provided fully explained solution: Let N's probability of winning any given game against G be g. Let N's probability of winning any given game against T be t. g>t because G is not as good a player as T. If the sequence of games is GTG, then N must win the game against T and either one of the two games against G. This probability is then t*(2*g-g^2). The subtraction of g^2 is to subtract out the double counting of winning both of these games. Likewise, if the sequence of games is TGT, then N must win the game against G and either one of the two games against T. This probability is then g*(2*t-t^2). The GTG probability comes out to 2*g*t - t*g^2, while the TGT probability comes out to 2*g*t - g*t^2. The first term in each of these is the same. The second, negative, term is larger when the g factor is squared than when the t factor is squared, so more is subtracted from the probability in the GTG case. So the probability of N winning is greater in the TGT case, and N should choose to play against T first.

	Subject	Author	Date
	solution	Charlie	2010-09-08 00:15:11
	re(2): Not so fast	ed bottemiller	2010-09-07 21:51:28
	Whose serve?	ed bottemiller	2010-09-07 16:40:22
	re: Not so fast	hoodat	2010-09-07 13:05:14
	Not so fast	Steve Herman	2010-09-07 12:47:18
	Solution	hoodat	2010-09-07 12:12:55
	solution	Daniel	2010-09-07 11:47:01