Imagine you are on a game show and there are three doors that you need to choose between: A, B, and C. Behind one of these doors is a car, and behind each of the others is a random object. Let's say you choose door A out of A, B, and C. The game show host then shows you that the car is not behind door B. Now you have the the opportunity to switch to door C or stay with door A. Do you switch, or do you stick with door A? Below are the tree diagrams of the decisions, with the doors having a goat if they don't have the car. In the basic tree, it shows all the possible outcomes with each choice. At the beginning there is a 1/3 chance of getting a car behind the door you choose and a 2/3 chance of a car not being there. But then, the host reveals one of the goats, taking it away from the possible outcomes. You then are trying to decide if you should switch doors or stay with the same one. The red X's show the possibilities taken away from the host and the purple X's are the outcomes taken away when you make a choice. When the host reveals a goat, there is still a 1/3 chance that there will be a car behind the original door you chose and a 2/3 chance it isn't behind it. However, a 2/3 chance that a car isn't behind the door you chose is also a 2/3 chance that the car IS behind the other door. If you stay with the same door, there is a 1:3 chance that you would get the car, but if you switch doors there is a 2:3 chance you get the car. You double your chance of winning if you switch doors. If you want to see a video explaining this phenomenon there is a great one below: http://www.stayorswitch.com/explanation.php
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AuthorIsabel Benak Archives
September 2018
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