Airplane Seating

The Question...

There are 100 seats on an airplane and they are all assigned. Each person who boards will take his assigned seat unless someone else is sitting in it, in which case he picks a seat at random. The first passenger to board is a little old lady who doesn't bother to look for her seat but sits in the first one she comes to. What is the probability that the last person to board will be able to sit in his assigned seat?

The Answer...