A line of 100 airline passengers is waiting to board the plain. They each hold a ticket to one of the 100 seats on that flight. (For convenience, let's say that the Nth passenger in line has a ticket for the seat number N.)

Unfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. All the other passengers are quite normal, and will go to their proper seat unless it is already occupied. If it is occupied, they will then find a free seat to sit in, at random.

What is the probability that the last (100th) person to board the plane will sit in their proper seat (#100)?

(In reply to Simpler solution by Richard Briscoe)

This is a great solution for a problem like this. The win condition is him sitting in his own seat, and the lose condition is him sitting in seat 100. Anything else is just extra junk, because the probability of him sitting in his own seat is equal to the probability of him sitting in seat 100.

Posted by Gamer on 2004-08-16 22:34:46