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?
