Before a knockout tournament with 2^n players I pick two players.
What is the probability that they have to play against each other
at some point in the tournament?
If the score is 8-8 do I have more chance of winning if the winner
is the first to reach 9 points or the first to reach 10 points?
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
A beats B by 2 choices to 1.
B beats C by 2 choices to 1
but A loses to C, again by 2 choices to 1.
Three voters go to vote in this election and have to rank the
candidates. First, check you agree that each voter has six possible
ways in which they can do this.
Assuming the voters are just as likely to rank them in one order
as another, what is the probability that they all vote in a way
that results in a paradoxical (intransitive) outcome?