Consider the following problem:
Order the passengers by the order they get on the plane.
Person 1 gets on the plane and takes a random seat.
Person 2 gets on the plane and takes his/her assigned seat if it is
available, or takes a random seat if not.
Person 3, ..., N-1 does as Person 2 does.
Person N takes the last seat remaning.
What is the probability that Person N gets his/her assigned seat?
Solution, with proof and fancy tree diagrams
Thanks to Scott Davis for posing this to me.