# A simple explanation to the Monty Hall problem

**Keywords: **
table stay, hard time, door, goat, change, question, car, matter, initial, choice, problem, monty, solution.
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The Monty Hall problem is an interesting probability question that people have a hard time understanding the solution. The problem is this: You are on a TV show and the there are 3 closed doors. Behind one of the doors is a brand new car, and behind the two other doors there is a goat. Obviously you want the car. So you make a choice. The door you chose remains closed but one of the other doors are opened and a goat is revealed (always). Now you are asked the following question: Would you like to change the door you selected, or stay with your initial selection? What should you do? does it even matter?

I've asked this question to a few people and all of them thought that it didn't matter. I had a hard time explaining to them that it did, until I saw this table which explains it all so nicely

In the table stay means choose door 1 and stay with your choice, change means choose 1 but change.

| door 1 | door 2 | door 3 | stay | change |
|--------|--------|--------|------|--------|
| car | goat | goat | cat | goat |
| goat | cat | goat | goat | car |
| goat | goat | cat | goat | car |

so you can see that unless you picked the car on your initial pick, you will get a goat 2/3 times if you don't change. The reason is that Monty always reveals the door with a goat behind it and of course never your selected door. Such a nice example of a table as a data visualization tool being useful.

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First published on 2015-07-16

Generated on May 29, 2024, 10:01 PM

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