Let's Do It! 8.4

There are three doors. Behind one door is a car. Behind each of the other two doors is a donkey. As a contestant, you are asked to select a door, with the idea that you will receive the prize that is behind that door. The game host knows what is behind each door. After you select a door, the host opens one of the remaining doors that has a donkey behind it. Note that no matter which door you select, at least one of the remaining doors has a donkey behind it for the host to open. The host then gives you the following two options:

1. Stay with the door you originally selected and receive the prize behind it.
2. Switch to the other remaining closed door and receive the prize behind it.

What is the probability of winning the car if you stay? What is the probability of winning the car if you switch? Will switching increase your chance of winning the car?

Try the simulation below to see which is the winning strategy.

How the simulation works:

1. Click on one of the doors. The computer will then open one of the remaining doors with a donkey behind it.
2. If your strategy is to remain with the original choice, click on that door again. That is, for example, if you clicked on door 2 first, click on door 2 again. If your strategy is to switch, click on the other door which is closed (not door 2).
3. The computer will keep a tally of each choice.

Did you find out the winning strategy? If not, click here.