There is a bus with 50 labelled seats from 1 to 50. There are also 50 persons labelled from 1 to 50 standing in a queue.
People board on the bus in sequence from 1 to n. The rule is, if a 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 50th person sits on his place i.e. 50th seat.