The Monty Hall Problem

Three DoorsThinking rationally is difficult. It requires you to be disciplined. You have to follow the rules even when you want to take the easy way out.

You have to follow the rules even when they completely go against your intuition.

In the same spirit as this post, let’s do a quiz.

You are presented with three doors.  Behind one door, there is a brand new car. Behind the other two doors, there are goats.  You are asked to pick one door.  You will receive the item that is behind the door that you choose.

After you pick the door, you are shown a goat behind a door that you did not choose.  This leaves two doors unopened.  The door you chose and one other door. You are then asked if you would like to switch your choice.

Would switching your choice help you win the new car?

Yes.  Switching your choice would increase your chances of winning the car.  You should always switch your choice.

Don’t believe me?  Test it out here.  If you run through the scenarios enough times, always switching your choice, you will get the car more often than if you never switched your choice.

Don’t feel bad if the answer does not make sense to you.  It does not make sense to most people, at first (including me).  You would think that the two doors left had a 50% chance of being either the car or the other goat.  But that is not the case.

The interactive feature that the New York Times created does a pretty good job of explaining it.  Just click on the “How It Works” tab to get the explanation.  The only way that you lose when you switch your choices is when you pick the car as your first choice.  And you have a 1/3 chance to pick the car as your first choice. You will always win if you switch your choice and you pick a goat for your first choice.  And you have a 2/3 chance of picking a goat as your first choice.

Photo courtesy of gfpeck 

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