This is a classic, and may have been posted here before, but if you haven't seen it, enjoy.
There is a 100-seat plane and 100 ticketed passengers with boarding passes that show their assigned seats.
The first passenger gets on, but can't find his boarding pass, so just sits in a seat at random.
Each subsequent passenger sits in their assigned seat if it is available, or else sits in a randomly chosen empty seat.
What is the probability that the 100th passenger to board will be sitting in his or her assigned seat?