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A friend of mine (an I.T. guy) gave me this tricky probability problem, that I couldn't solve.

$n$ persons go to a cinema that has $n$ seats, and everyone of them has an assigned position written on the ticket.

The first person $p_1$ commits an error and chooses the wrong seat.

Then $p_2,\ldots,p_n$ arrive (in order) and they choose their seat according to the following rule:

"If the assigned seat is free, go there. Otherwise, choose a random seat among the free ones."

What is the probability for the last person $p_n$ to sit in his assigned seat?

Paglia
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    http://math.stackexchange.com/questions/5595/taking-seats-on-a-plane – Marc Mar 23 '14 at 18:35
  • thank you! this is slightly different, in the sense that the choice of $p_1$ is fixed, but should be easy now to adapt the answer... – Paglia Mar 23 '14 at 18:43

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