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)?

you can't have a 50% chance that the seat
is not taken

IT IS ONLY A 50% chance IF AND ONLY IF

THE SECOND LAST PASSENGERS SEAT IS TAKEN
AND THE LAST PASSENGERS SEAT IS FREE

Posted by quddous behrouzi on 2002-06-21 09:59:32