A line of <i>n</i> airline passengers is waiting to board a
plane. they each hold a ticket to one of the 100 seats on that
flight. The <i>i</i>th passenger in line has a ticket for the seat
number <i>i</i>.
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Unfortunately, the first person in line is crazy, and will ignore the
seat number on his ticket, picking a random seat to occupy. All the
other passengers are quite normal, and will go to their proper seat
unless it is already occupied. If their given seat is occupied, they
will then find a free seat to sit in, (uniformly) at random.  What is
the probability that the last (<i>n</i>th) person to board the plane
will sit in their proper seat (#<i>n</i>)?