Question 3: Donald Trump wants to hire two secretaries. There are n applicants a, a2,..., an for these jobs, where n 2 is an integer. Each of these applicants has a uniformly random birthday, and all birthdays are independent. (We ignore leap years.) Since Donald is too busy making America great again, he does not have time to interview the applicants. Instead, he uses the following strategy: If there is an index i such that ai and a;+1 have the same birthday, then he chooses the smallest such index i and hires a, and ai+1. In this case, the hiring process is a success. If such an index i does not exist, then nobody is hired and the hiring process is a total disaster. Determine the probability that the hiring process is a success.