B. 4771. In an aeroplane, there are one hundred seats, booked by one hundred passengers, each having their assigned seat. However, the first passenger does not care, and sits down on a random seat. When the other passengers enter one by one, each of them tries to take his or her own seat, or, if that seat is already taken, selects another one at random. What is the probability that the hundredth passenger is able to take his own seat?
Proposed by N. Nagy, Budapest
Deadline expired on 10 March 2016.