Friday, February 6, 2009

The Monty Hall Problem

It's 1975 and you are dressed as a chicken attending Let's Make a Deal with Monty Hall. Monty picks you and offers you the choice of 3 doors - behind 1 door is a new car, behind the other 2 doors are goats. You choose your door and Monty, knowing what's behind the doors, opens a door you didn't choose revealing a goat (in the game, he always reveals a goat behind one of the unselected doors to raise suspense). He then asks you if you want to change your choice and switch to the other remaining door. He taunts you by calling you a chicken. Should you switch? Does it matter?

In fact, it does matter and you should switch doors. By switching, you double your chances of winning the new car. This may seem crazy, how could your odds be anything other than 50-50? That's the Monty Hall problem - the famous, confounding probability paradox.

Continue for an explanation and a diagram.