A line of n airline passengers is waiting to board a plane. they each hold a ticket to one of the 100 seats on that flight. The ith passenger in line has a ticket for the seat number i.

Unfortunately, the first person in line is crazy, and will ignore the seat number on his ticket, picking a random seat to occupy. All the other passengers are quite normal, and will go to their proper seat unless it is already occupied. If their given seat is occupied, they will then find a free seat to sit in, (uniformly) at random. What is the probability that the last (nth) person to board the plane will sit in their proper seat (#n)?