Probability Problem - Can you solve it?

39. Probability Problem

I just had a "Discussion" with the missus about this one. So I thought I'd throw it open to all! :)

You are on an American game show. During the show you would be faced with 3 doors, behind 2 doors were goats and behind the third was a car. After you picked a door and before the door was opened, the host would open another door and showed you a goat (he knew where the car was so he always showed you a goat). He then asked if you wanted to stick to your original choice or switch to the other unopened door.

So, should you stay with the door you originally chose or should you switch to the other door? It is assumed you want the car!

Mark

Submitted by mtiller · Added 26 August 2016

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Solution:

You should always switch to the other door. Initially, you have a 1/3 chance of picking the car and a 2/3 chance of picking a goat. When the host reveals a goat behind one of the other doors, switching gives you the 2/3 chance of winning the car, while sticking with your original choice keeps you at 1/3. If you originally picked a goat and then switch, you will get the car, which is why switching is the better strategy.

Comments (1)

Wikonimo 30 December 2016

If you switch, there is a 2/3 chance that you will get the car.

For the first choice, there is a 2/3 chance of choosing a goat, and a 1/3 chance of choosing a car. Once the goat is revealed, once of the doors hides a goat, the other hides the car. If you originally picked a goat and then switch, you will get the car. If you originally picked the car, you get a goat. But there was a 2/3 chance of originally getting a goat, so you switch to get a 2/3 chance of getting the car.

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