There are 100 passengers waiting in line to board an airliner with 100 passenger seats. The seats are numbered from 1 to 100. Each passenger holds a ticket with his seat number. You are the last passenger in line. One of the passengers ahead of you in line is crazy. We don’t know which one. He will ignore his seat assignment and sit in a random empty seat (the crazy person might sit in his assigned seat; he is equally likely to sit in any open seat). Every other passenger will sit in their assigned seat — unless it is already taken, in which case they too will sit in a random empty passenger seat. Passengers board one by one. What is the probability that you will sit in your assigned seat?