Today, as one of the final examples of probability, we discussed the famous Monty Hall Problem (named after the host of the old game show "Let's Make a Deal"), which is described in detail here. To my mind, the clearest explanation of the surprising solution is that given by Leonard Mlodinow's book The Drunkard's Walk. Based on Mlodinow's writing, here's a diagram we created in class (thanks to Kristina for taking the picture):


The basic idea is that scenarios in which switching helps occur twice as often as ones in which switching hurts.

UPDATE (Dec. 19, 2011): I learned of a Mythbusters TV episode, in which the Monty Hall Problem is demonstrated (thanks to Kaitlin Leckie). Here is a video clip; the most useful part, in my view, starts at the 6:30 point.