A classic probability problem that defies intuition: the answer is the same for any number of passengers, and arriving at it requires looking at the problem from the right angle.
The last passenger
Riddle statement
A plane has \(n\) seats and \(n\) passengers, each with their assigned seat.
Passenger 1 loses his card and sits randomly in any seat. Starting with passenger 2, each one acts like this:
- if his seat is free, he sits in it;
- if it is occupied, he chooses at random from the free seats.
What is the probability that the last passenger ends up in his own seat?