Yesterday I gave a mini-lecture in our teaching seminar on Bayes' theorem motivated by the "Monty Hall Problem":
Suppose you are on "Let's Make a Deal" gameshow, and you are given the choice of three doors: behind one door is a new car; behind the others are goats. You pick a door, say door #1, and Monty Hall, the host, who know knows what's behind the doors, opens another door, say door #3, and reveals a goat. He then says to you, "Do you want to stay with door #1, or switch to door #2?" Is it to your advantage to switch your choice?
If your initial guess is you have a 50/50 chance on winning the car regardless if you choose door #1 or door #2 knowing there is a goat behind door #3, think again. A simple application of Bayes' theorem will show that the probability of winning the new car by switching from door #1 to door #2 is 2/3. Therefore, it's to your advantage to switch your choice. Discuss.
