Checkpoint 4.9.7. 100 people on an airplane with boarding pass issues.
This is a famous problem. 100 people are in line, boarding an airplane 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?