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, she will pick the first city that is better than all previous cities. The cities are interviewed in a uniformly random order. 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.

You should arrive at an exact answer for the probability in terms of a summation. Approximate your answer using ni=1 i1 ln n and find the optimal value of m that maximizes the probability that the best city is selected. You can also say ln(n 1) ln n.