The Monty Hall Problem

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Have you ever seen the game show “Let’s make a deal” hosted by Monty Hall? My guess is that your answer is “Yes” for the show but a firm “NO” for the host. This show aired in the 1960s, making it one of the oldest game shows presented on tv.

On this show, a participant was asked to choose between three doors. Two doors having a goat behind it, while the remaining one having a brand-new car.

If you are a participant, you would want to be smart because between the choice of a goat and a car, you would probably want a car. Mathematically, the probability of choosing a car is 1/3, and with no information pointing to which door is ideal, a blind guess is inevitable. So, you choose door “1”.

After your choice, you are told that behind door 3, there is a goat. Then, the host asks if you want to switch your answer to door 2 or stay with door 1? What should you do?

The probability of getting a car is now 1/2 as there is now one goat and one car. At first glance, it does appear as a blind guess as there is still a 50/50 chance of it being a goat. Would you switch or would you stay with your initial choice? What if I told you, if you switch, you have a higher chance of winning the car.

The reason being that the probability of 1/2 is wrong. When you first chose between 3 doors, there was a 1/3 chance of getting a car. After a door with a goat is revealed, it doesn’t change the fact that you made the initial choice with a 1/3 probability. With two doors, it is still a 33.33% chance that you have chosen a car and a 66.66% chance that you have chosen a goat. This means that the other door has 66.66% chance of having a car or 33.33% chance of having a goat.

Though masked with an illusion, if given the choice, you must always change your option to win the prize!


Reference:

Car Image: https://www.123rf.com/stock-photo/2d_car.html?sti=mc1dboesuoqkybtcnc|

Goat Image: https://3dwarehouse.sketchup.com/model/ueea78486-e06e-4238-9cf6-e1403365ffd6/2D-GOAT


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