Wednesday, January 02, 2008

Sold Out Flight

On a sold out flight, 100 people line up to board the plane. The first passenger in the line has lost his boarding pass, but was allowed in, regardless. He takes a random seat. Each subsequent passenger takes his or her assigned seat if available, or a random unoccupied seat, otherwise. What is the probability that the last passenger to board the plane finds his seat unoccupied?


  1. would it be 100% if the seats are sold out- all that could be left was his seat?!

  2. my bad- i read the question wrong. i thought it said if there WOULD be a seat LEFT for him to have! oops!!!

  3. When the last passenger boards the plane, there are just two possibilities: the one remaining seat may be his or that of the first passenger Under the assumption that no preference has been exhibited by the boarding passengers towards either of the two seats, they both have the same probability to become the last unoccupied seat: 50%.

    What do you think? Does this make sense?


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