An airplane has 100 seats and is fully booked. Every passenger has an assigned seat. Passengers board one by one. Unfortunately, passenger 1 loses his boarding pass and can't remember his seat. So he picks a seat at random (among the unoccupied ones) and sits on it. Other passengers come aboard and if their seat is taken, they choose a vacant seat at random. What is the probability that the last passenger ends up on his own seat?