Soccer
Source: 2006 AIME II 10
March 28, 2006
probabilitysymmetrynumber theoryrelatively primeAMC
Problem Statement
Seven teams play a soccer tournament in which each team plays every other team exactly once. No ties occur, each team has a chance of winning each game it plays, and the outcomes of the games are independent. In each game, the winner is awarded a point and the loser gets 0 points. The total points are accumilated to decide the ranks of the teams. In the first game of the tournament, team beats team . The probability that team finishes with more points than team is , where and are relatively prime positive integers. Find .