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?