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The Monty Hall Problem

 
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This is interesting. You might remember Let's Make a Deal.

Suppose there are three closed doors.
There's a goat behind two of them, and a good prize behind one.
You make a choice.
One of the doors that has a goat is now opened.
You are asked if you want to change your choice to the other unopened door.
VERY counter-intuitively your odds of getting the good prize increase if you do change your choice.

https://en.wikipedia.org/wiki/Monty_Hall_problem
 
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Guillermo Ishi wrote:
VERY counter-intuitively your odds of getting the good prize increase if you do change your choice.



To me, it was never counter intuitive. I think that this is also why they don't offer the option to change the choice anymore.

Henry
 
Guillermo Ishi
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Here was my original reasoning.

You pick a door -- odds are 1/3 you're right
Goat is revealed and door is thrown out
The odds you have the right door are now 1/2 -- two possibilities, one winner. Thus nothing to be gained by switching doors.

Does that fix you and make it counterintuitive?

 
Henry Wong
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Guillermo Ishi wrote:Here was my original reasoning.

You pick a door -- odds are 1/3 you're right



Correct. The odds that you picked the right door is one out of three. And the odds that the prize is in one of the other two doors is two out of three. Also, only one of the other two doors contain the prize.

Guillermo Ishi wrote:
Goat is revealed and door is thrown out
The odds you have the right door are now 1/2 -- two possibilities, one winner. Thus nothing to be gained by switching doors.

Does that fix you and make it counterintuitive?



Incorrect. You did not choose the door that is thrown out. It was chosen by the show, that know which is the prize and which is not the prize. So, the odds does not change. The show simply showed you the door, out of the two that you did not pick, that was not the prize.

Henry
 
Guillermo Ishi
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The intuitive thing is to think the game has restarted with two doors, when it arrives at the two closed doors.
 
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