The famous Monty Hall paradox

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Introduction

Imagine you are in a game show called "Let's make a deal" on television with the chance to win a brand new sports car. The car is behind one of the 3 doors, behind the other 2 doors are goats (or donkeys). After you chose your door the game master (Monty Hall, who knows the location of the car) opens one of the 2 other doors with a goat behind it. Do you stick with the door your first choice, or do you switch to the other one? Does it even matter?

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What you should do

At the beginning there is a 1/3 chance the car is behind the door. But whenever the game master reveals a door with a goat behind the odds change. It is not a 1/3 and 1/3 chance nor a 1/2 and 1/2 chance, but a 1/3 and 2/3 chance of winning the car.  Whenever the game master opens a door with a goat, he adds critical value. The initial door you chose still has a probability of 1/3 but the other door you didnt choose now has a probability of 2/3 (because the other unchosen door has definitely a goat). The pictures below explain this. 

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Another way of visualising this is trough a probability diagram. 

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Surprisingl, you should always switch doors since this increase your chance of winning. The odds aren't 50-50, if you switch you'll have a chance of 2/3 to win the car. At first sight this seems absurd, this is why the problem became a paradox.

If you want you test it here

Sources

https://betterexplained.com/articles/understanding-the-monty-hall-problem/

https://en.wikipedia.org/wiki/Monty_Hall_problem

http://mathworld.wolfram.com/MontyHallProblem.html