March Madness Coin Toss Tournament 2
In a coin toss tournament, players are placed in a single-elimination playoff tree. For each game in each round, 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 player left who is then declared the winner.
What is the probability that you will correctly predict the outcome of all players in the tournament? The probability can be expressed as . Enter as your answer.
The answer is 63.
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1 solution
There are 3 2 coin flips to determine the winners of the first round, then 1 6 coin flips for the second round, then 8 , then 4 , then 2 , and then 1 , for a total of 3 2 + 1 6 + 8 + 4 + 2 + 1 = 6 3 coin flips for the whole tournament. Since each coin flip has 2 outcomes, there are 2 6 3 possible outcomes for the tournament, so you have a 2 6 3 1 chance of correctly predicting the outcome of all 6 4 players in the tournament, which means x = 6 3 .