Coding Horror: Monty Hall, Monty Fall, Monty Crawl A variation on a classic probability riddle. Wikipedia has
a good writeup on it, but if you haven't seen it before, I suggest trying to solve it first. Hopefully, we'll have a million people yelling at each other why they're wrong.
Monty Hall Problem: Suppose the contestants on a game show are given the choice of three doors: behind one door is a car; behind the others, goats. After a contestant picks a door, the host, who knows what's behind all the doors, opens one of the unchosen doors. The door the host opens is intentionally a goat; he would never pick the door with the car. He then asks the contestant, "Do you want to switch doors?" What are the probabilities for winning the car for switching doors or staying with your first pick?
Monty Fall Problem: In this variant, once you have selected one of the three doors, the host slips on a banana peel and accidentally pushes open another door, which just happens not to contain the car. Now what are the probabilities that you will win, either by sticking with your original door, or switching doors?
Monty Crawl Problem: Once you have selected one of the three doors, the host then reveals one non-selected door which does not contain the car. However, the host is very tired, and crawls from his position (near Door #1) to the door he is to open. In particular, if he has a choice of doors to open, then he opens the smallest number available door. (For example, if you selected Door #1 and the car was indeed behind Door #1, then the host would always open Door #2, never Door #3.) Now what are the probabilities that you will win the car if you stick versus if you switch?