Probability of Sitting in a Seat [duplicate]

Possible Duplicate:
Taking Seats on a Plane

The 120 seats on a Northeast Airlines flight were completely booked, with each of the 120 passengers having different assigned seats. The passengers entered the plane one-by-one. Unfortunately, the first passenger couldn’t read their boarding pass and sat in a (uniformly) random seat. Each subsequent passenger sat in their assigned seat if it was available when they entered and sat in a (uniformly) random empty seat otherwise. What is the probability that the last passenger sat in their assigned seat?

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marked as duplicate by Aryabhata, Did, Henry, Rudy the Reindeer, Martin SleziakJan 25 '12 at 8:14

The usual intuition about this problem is to think that the answer must depend on the number $n$ of passengers/seats (and oddly, people often suggest that the probability is $\frac1n$...). Curious to know how your intuition leads you to the answer $\frac12$. –  Did Jan 25 '12 at 8:00