March Madness Coin Toss Tournament

Probability Level 2

In a coin toss tournament, 64 64 players are placed in a single-elimination playoff tree. For each game in each round, 2 2 players face each other and an impartial referee flips a fair coin to decide on one player to be eliminated from the tournament and the other player to move on to the next round. This process continues until there is 1 1 player left who is then declared the winner.

If you are one of the players in the coin toss tournament, what is the probability that you will win? The probability can be expressed as 1 2 x \dfrac{1}{2^x} . Enter x x as your answer.


The answer is 6.

David Vreken by David Vreken , 42, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Jordan Cahn
Mar 14, 2018

Since the situation is perfectly symmetric, every player has an equal probability of winning. Thus the probability that you win is 1 64 = 1 2 6 \frac{1}{64}=\frac{1}{2^6} .

Alternatively, note that there are six rounds in the tournament and you have a 1 2 \frac{1}{2} probability of winning each round. Thus the probability of winning the tournament is ( 1 2 ) 6 = 1 2 6 \left(\frac{1}{2}\right)^6=\frac{1}{2^6} .

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Good solution!

David Vreken - 3 years, 2 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...