There are N players in a tennis tournament. Assuming the initial pairings are done randomly, what are the odds that a certain pair will play each other?

(In reply to The full tournament by Charlie)

Charlie, I´m not succeeding in find the answer.

Your answer is 2/N.

This means that for 2 players, P = 1, which is obvious.

But, for N = 4, your answer would be 2/4 = 1/2.

In the first round the odds are 1/3 of the two play each other, and 2/3 for they do not play each other. Thus, in the second (and last round, when there are only 2 players), the odds are the product of (prob of they did not play each other in the first round x prob of they play in the second round), which gives : 2/3 * 1 = 2/3.

Where am I wrong?

 

Posted by pcbouhid on 2005-08-04 20:10:41