Right! I know in my own head why the probability of getting the car by switching is 2/3.
Pick a Door.
Probability of the car being behind that door is 1/3.
Probability of the car being behind either of the other doors is 2/3.
NOW - instead of having an incorrect door being opened, imagine that the two unchosen doors merge into one big door. If you open this door and the car is behind it you get the car (AND the goat that is with it if you really want it).
What is the probability that the car is behind this new mega-door? If you said 1/2 then you are wrong. It is still 2/3.
Do you want to swap from your chosen door now?
Merging the two unchosen doors is logically the same as revealing one of the unchosen doors as having a goat. It may take some thought to accept this but now in my head I know what is right and this tallys with what my program said.
QED
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