# Problem B. 4771. (February 2016)

**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

(5 pont)

**Deadline expired on March 10, 2016.**

### Statistics:

112 students sent a solution. 5 points: 65 students. 4 points: 16 students. 3 points: 7 students. 2 points: 3 students. 1 point: 10 students. 0 point: 10 students. Unfair, not evaluated: 1 solution.

Problems in Mathematics of KöMaL, February 2016