Brain teaser.

There are 100 guys boarding a plane one at a time. This not being Southwest, they all have assigned seats, and there are 100 passenger seats on this plane, exactly one for each passenger.

The first person to board the plane decides not to pay attention to his ticket and just sit anywhere randomly. Every person that follows first tries to sit in his assigned seat. If that seat is taken, he sits in one of the unoccupied seats chosen at random.

The next person does not enter the plane until the previous person is fully seated, so there are no multithreading issues. The question is, what is the probability that the last person to board the plane sits in his assigned seat?