Last two students sitting in the right place
Source: IMS 2009
May 20, 2009
probabilitysymmetryprobability and stats
Problem Statement
Suppose that there are 100 seats in a saloon for 100 students. All students except one know their seat. First student (which is the one who doesn't know his seat) comes to the saloon and sits randomly somewhere. Then others enter the saloon one by one. Every student that enters the saloon and finds his seat vacant, sits there and if he finds his seat occupied he sits somewhere else randomly. Find the probability that last two students sit on their seats.