Suppose n players enter a tournament. If n is even, then in the first round, players are paired against one another randomly to play a match. Assumeall players are equally skilled so that when any two play a match, the winner is determined randomly. The loser in each pair is eliminated, and the winnerin each pair continues to the next round. If n is odd, then one player isselected at random to bypass to the second round without playing a match. The remaining players are put into a common room, where this procedureis repeated. Repeat this procedure until a single individual remains. Given two players A and B, write the probability that A and B ever play against each other in the tournament.