100 people are in line, boarding an aeroplane with 100 seats, one at a time.
They are in no particular order.
The first person has lost his boarding pass, so he sits in a random seat.
The second person does the following:
Goes to his seat (the one it says to go to on the boarding pass).
If unoccupied, sit in it.
If occupied, find a random seat to sit in.
Everyone else behind him does the same.
What is the probability that the last person sits in his correct seat?