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No, because the host never tells the truth. Door 2 has a goat, door 1 is a 50/50 chance to be a car

The accepted answer is you have a 2/3 chance of getting the car if you swap doors, and only a 1/3 chance of the car if you stay. Counterintuitive yeah? The reason is that the host will never pick the door with the car, obviously, as that would be cheating. He always picks a 'goat' door. Because there's a 1/3 chance you originally picked a car, it means the other 2 doors have a 2/3 chance of being the car, and because the host has shown a goat door already, the other door holds the 2/3 chance alone.

Anyway, that's the accepted answer, but there's disagreement. The question actually states the host specifically picks door 3, which has a goat. This is not the same thing as "the host picks whatever of doors 2 and 3 has the goat".If we assume that he only picks a door if it's 3 and the goat, this changes the probability to 1/2 either way.

I had to draw this out to get it the first time the supposed smartest person in the world, Marylin Vos Savant, explained it. Her answer is 2/3, but I don't think she takes into account the specifics of the scenario :cool:
 

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