In a 4 round chess tournament with 16 players (where the loser of each two player match is eliminated and the winner moves on to the next round), the pairings for all matches are decided randomly. The competing players all have different rankings and in any given match the higher ranked player always wins. What is the probability that the player with the second highest ranking is the losing finalist?
The answer is:
The reason is:
The only way for the rank 2 player to get to the finals is if the rank 1 player is in a different half of the tournament. There are 16*15 ways of arranging these two players, and 16*8 of those put the two in different halves. So the final answer is (16*8)/(16*15) = 8/15.