Chess Tournament | BRAINSTELLAR

probability puzzles


A chess tournament has KK levels and N=2KN = 2^K players with skills P1>P2>...>PNP_1 > P_2 > ... >P_{N}. At each level, random pairs are formed and one person from each pair proceeds to the next level. When two opponents play, the one with the better skills always wins. What is the probability that players P1P_1 and P2P_2 will meet in the final level?