Man on a Plane Probability (in the wild)
My friend had an interview with Google during which they asked him this interesting question:
A man gets on a plane with n seats, but he has lost his ticket. So this man randomly chooses a seat. The next guy gets on the plane with his ticket. He goes to his seat, if it is empty, he sits there. If it is taken, he randomly chooses a seat. This continues until n-1 seats are filled. The n-th person enters the plane with his ticket. He goes to his seat. What is the probability that it is empty?