Interview Puzzles :: Discussion

Chaos in the bus

There is a bus with 100 labeled seats (labeled from 1 to 100). There are 100 persons standing in a queue. Persons are also labeled from 1 to 100.

People board on the bus in sequence from 1 to n. The rule is, if the person ‘i’ boards the bus, he checks if seat ‘i’ is empty. If it is empty, he sits there, else he randomly picks an empty seat and sits there. Given that 1st person picks seat randomly, find the probability that 100th person sits in his place i.e. 100th seat.