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)?

i believe that the probability is a slim 50-50 chance. either the crazy ass passenger will go over 2 his own seat or he'll sit @ some one else's seat. then the person who's seat is taken will go sit @ the crazy person's seat. so this means that the 100th person will b given a 100% chance of getting 2 his own seat, unless the crazy person sits @ his seat. this will mean that that's a 50-50 chance. the crazy person will still have 98 more people 2 bother (not counting himself and the 100th person). that's about it. peace out!!!

Posted by omar on 2004-02-21 15:43:24