When i posted my review about the movie “21,” i mentioned the Monty Hall problem presented in the movie. I intended to follow-up with the answer and forgot about it until today. Here’s a restatement of it::
You’re on the gameshow Let’s Make a Deal and are present with 3 doors. You’re told behind one is a brand new car, and behind the other two are goats. You choose a door, say Door A. Monty (who knows which door the car is behind) then reveals what is behind Door C – a goat. And he says to you, i’ll give you a chance to switch your choice to Door B. Do you switch doors?
Most people reason that there is an equal chance that the car is behind Door A and Door B, so there’s nothing to be gained by switching. Plus, there is a psychological warning in your head telling you that if Monty is suggesting that you switch, it must be bad for you to do so. So your gut instinct is to stick with your original choice.
Monty Hall problem
The correct answer is to switch doors. The car is twice as likely to be behind Door B than your original choice of Door A.
When you made your original selection, you had a 33.3% chance of getting it right. Which means a 66.6% chance of being wrong. That has not changed just because one of the doors has been opened. Your door still has a 33% chance of containing the car. But Door B is now 66.6% likely to contain the car. Switch!!
Pretty cool problem. If you don’t believe me – look it up.