Math Is Fun Forum

jonny

Guest

knock out tournament

A tennis tournament for 2^n players is organised as a knock-out
tournament with n rounds, the last round being the final. Two players
are chosen at random. Calculate the probabilities they meet

a) in the first round
b) in the final
c) in any round

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: knock out tournament

Hi;

Standard book problem straight from my notes copied from some book.

There are

ways to pair off 2^n players. Each round 1/2 of the players are eliminated, First round 2^(n-1) players are paired. Then 2^(n-2) player, 2^(n-3) until we get to the final round when two players are playing.

a)

b)

c)

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