Carlos and Michael are participating in a tennis tournament that has 16 players

Question

Carlos and Michael are participating in a tennis tournament that has 16 players including them. The tournament ladder is shown below. The winner of any match advances to the next round while the loser is eliminated. Assume that the initial draw is random and unbiased. Assume also that all the 16 players are evenly matched (i.e., when any two of them meet, either one can win with probability 1/2). Compute the probability that Carlos and Michael meet in the tournament. Repeat part (a) if the number of players is 2^n rather than 16.

Explanation / Answer

n!(r!(nr)!n!(r!(nr)!

=16! / (2!(162)!))

= 120

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