100 passengers

This is an article I posted earlier on a previous version of my blog. It’s about an interesting puzzle that goes like this:

Imagine a plane with a hundred seats. There are also a hundred passengers for this fully booked plane. Each passenger has a ticket indicating his or her seat number. However, the first passenger lost his ticket and takes a random seat. The other passengers enter the plane one by one and they either take their legitimate seat (if it’s not taken) or a random seat (if their seat is taken). The question is: what are the odds for the last person to be able to take the seat matching his seat number?