Maths Puzzle :: Discussion

The Hilton Hotel reserves all its 101 rooms for travelers and each guest is assigned a room in advance. The first guest arrives but has forgotten his room number. The hotel clerk, who does not have access to the reservations book, randomly puts him in one of the rooms. As the rest of the guests arrive they are given their reserved room if available or if already taken, are given a random empty room. What is the chance that the 101st guest gets her
reserved room?