100 people are waiting to board a plane. The first person's ticket says seat 1; the second person in line has a ticket that says seat 2, and so on until the 100th person, whose ticket says seat 100. The first person ignores the fact that his ticket says seat 1, and randomly chooses one of the hundred seats (note: he might randomly choose to sit in seat 1). From this point on, the next 98 people will always sit in their assigned seats if possible; if their seat is taken, they will randomly choose one of the remaining seats (after the first person, the second person takes a seat; after the second person, the third person takes a seat, and so on). What is the probability the 100th person sits in seat 100?