Who Took My Seat?!?!
For this problem, consider an airplane with one hundered seats. Every
seat has a passenger that is assigned to sit in it and the passengers
file in one at a time to take their seats. The first person gets on the plane
and realizes he can't read what seat number is his. So, he picks a random
seat out of the 100 seats on the plane. Now, each passenger after this
boards the plane and, if their seat is already taken, will pick a random
seat out of what ever is left. If their seat is empty,
then of course they sit in their own seat. Here is the question:
what is the probability that the last person to board the plane will sit
in their own seat?
Hint: There is a bit of useless information in the problem....