A tennis tournament is organized for \(2^n\) players where each round is single elimination with \(n\) rounds. Two players are chosen at random.

- What is the chance that they meet in the first round or second round ?
- What is the chance they meet in the final or semi-final ?
- What is the chance they do not meet at all ?

[Sudov and Kelbert, p4 problem 1.2]