Problem 13. Airplane Seats
143 people are in line to board a plane. Each person has a different seat number between 1 and 143. The number of seats in the plane is exactly 143. The first person loses his ticket and sits on a random seat. From then on, everyone sits on their own seat unless someone else is already sitting there, in which case they sit on a random empty seat. What is the probability that the 143rd person sits on his own seat?
Link to the problem on Twitter: https://twitter.com/Riazi_Cafe/status/1678051790208548865
. The answer to the question is 1/2.
Assume that the first and last person exchange their seat numbers. In this case, if the last person was sitting on his own seat in the previous case, he will not sit on his own seat now and vice versa. Therefore the number of cases in which the last person sits on his own seat is equal to the number of cases wherein the last person does not sit on his own seat.
Link to the solution on Twitter: https://twitter.com/Riazi_Cafe/status/1678537566969004033