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There is an airplane and 100 passengers are given boarding pass for the same. The first passenger lost his boarding pass and he did not remember the seat number assigned to him. So, when this first passenger boards the plane he chooses one seat uniformly randomly. Rest of the passengers, board the plane in the sequence of 2 to 100. If a passenger finds his seat vacant, he will sit there, if not, he chooses a vacant seat uniformly randomly. The question is, what is the probability that the last person ( 100th in this case ) will find his seat vacant when he boards the plane?
Number 100 has nothing to do with the puzzle and we can as well state that there are n passengers.
http://sbjoshi.wordpress.com/2008/05/28/puzzle-kis
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