Difference between revisions of "2006 AIME A Problems/Problem 10"

Latest revision as of 10:33, 22 August 2009

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-== Problem ==
+#REDIRECT [[2006 AIME I Problems/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 <math> 50\% </math> 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 <math> A </math> beats team <math> B. </math> The probability that team <math> A </math> finishes with more points than team <math> B </math> is <math> m/n, </math> where <math> m </math> and <math> n </math> are relatively prime positive integers. Find <math> m+n. </math>
-== Solution ==
-== See also ==
-*[[2006 AIME II Problems]]