People often like to say things along the lines of “Well, we're either gonna win the game, or we're not.  So I'd say the odds are fifty-fifty."  This is, of course, rarely the case.

We will look at some problems and try to determine what the odds really are. Consider the following problem. A plane has 100 seats and 100 passengers. They enter the plane, one-by-one, in order. The first passenger is lazy and selfish, and picks a random seat to sit in. The rest of the passengers try to sit in their assigned seats, but if they find another passenger there, they choose another seat at random. What are the odds that the last passenger sits in his/her assigned seat?