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Six teams play a single round-robin tournament, in which each team plays every other team exactly once, there are no ties, and for each team, the probability of winning any given game is 1/2. What is the probability that at least two different teams finish the tournament with the same number of wins? Express your answer as a common fraction.

 Oct 5, 2024
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The six teams play C(6,2) = 15 games.

 

Therefore, the probability that at least two different teams finish the tournament with the same number of wins is 1 - 15/2^15 = 32753/32768.

 Oct 5, 2024

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