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Monty Hall Problem


Dr. Pomade

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I think of it as being able to pick 2 doors instead of one when asked to switch.

 

With your first pick you have 1/3 chance of having the car. The other two doors have 2/3 chance of the car. Revealing that one of the other two doors does not have the car doesn't change the chance that those two together had 2/3 chance of the car, so now the unopened door you didn't pick is 2/3 chance by itself - since the host will always open a door containing the goat. The revealed door is not picked at random so that is why it can "modify" the chances.

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What would you do op?

 

I would always switch doors.

 

This is my reasoning. If you don't switch doors, then you have a 50% chance of getting the car. (Actually, it's only 1/3, but when the other goat is revealed then I know I at least have a 50-50 shot that my door hides the car.) However, if you switch doors, then you have a 67% percent chance of getting the car.

 

If you switch doors, there are only three outcomes possible, and 2 of the 3 result in you getting the car.

 

1: you picked a goat. Goat revealed. You switch and get the car.

 

2: you picked the other goat. Goat revealed. You switch and get the car.

 

3: you (were unlucky enough to have) picked the car. Goat revealed. You switch and get the goat.

 

At the get-go, what are you more likely to pick - a goat or a car? Well, your odds are 2/3 for a goat and only 1/3 for a car. By switching your pick after a goat is revealed, you get to flip those odds in your favor: 2/3 of the time you'll get the car and only 1/3 will you switch and get a goat.

 

This is what I tried to explain to my friend, who, by all accounts, is a highly intelligent, very accomplished individual. (He has a doctorate in psychology and a law degree as well.) However, he was having none of it, and argued vehemently that there was no statistical advantage to switching.

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This is what I tried to explain to my friend, who, by all accounts, is a highly intelligent, very accomplished individual. (He has a doctorate in psychology and a law degree as well.) However, he was having none of it, and argued vehemently that there was no statistical advantage to switching.

 

There are a couple of reasons for arguing. The first, for me, is to bring my point of view to someone else so they can see they're wrong. If this is not possible, I argue loudly so other people can see they're ignorant and I am smarter.

 

If neither of these things will happen I stop arguing, and just tell people they're right, and they are happy in ignorance.

 

Sometimes I am the other person in this scenario.

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There are a couple of reasons for arguing. The first, for me, is to bring my point of view to someone else so they can see they're wrong. If this is not possible, I argue loudly so other people can see they're ignorant and I am smarter.

 

If neither of these things will happen I stop arguing, and just tell people they're right, and they are happy in ignorance.

 

Sometimes I am the other person in this scenario.

 

:lol:

 

You're brilliant.

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By even posting that, you fall into another category...

 

:no:

 

...a highly intelligent... individual. (He has a doctorate in psychology...)

Isn't that an oxymoron?

 

There are a couple of reasons for arguing. The first, for me, is to bring my point of view to someone else so they can see they're wrong. If this is not possible, I argue loudly so other people can see they're ignorant and I am smarter.

 

If neither of these things will happen I stop arguing, and just tell people they're right, and they are happy in ignorance.

 

Sometimes I am the other person in this scenario.

 

:lol:

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