The NBA is looking to expand to another city. In order to decide which city will receive a new team, the commissioner interviews potential owners from each of the N potential cities (N is a positive integer), one at a time. Unfortunately, the owners would like to know immediately after the interview whether their city will receive the team or not. The commissioner decides to use the following strategy: she will interview the first m owners and reject all of them (m € {1,...,N}). After the mth owner is interviewed, s/he will pick the first city that is better than all previous cities. The cities are interviewed in a uniformly random order. Required:
What is the probability that the best city is selected? Assume that the commissioner has an objective method of scoring each city and that each city receives a unique score.