2006 AIME II Problem 10

Seven teams play a soccer tournament in which each team plays every other team exactly once.
No ties occur, each team has a 50 \% chance of winning each game it plays, and the outcomes of the games are independent.
In each game, the winner is awarded 1 point and the loser gets 0 points. The total points are accumulated to decide the ranks of the teams.
In the first game of the tournament, team A beats team B.
The probability that team A finishes with more points than team B is m / n, where m and n are relatively prime positive integers.
Find m+n.