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each door has a 1/3rd chance of the car. you choose 1.

there’s a 1/3rd chance you’re right (door 1 wins), a 2/3rd chance you’re wrong (door 2 or 3 wins)

host opens door number 3. reveals a goat.

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–g

the chances of doors 2 or 3 combined having the car (and thus, you being wrong) has not changed. it’s still 2/3rds.

just because one of those two doors has been revealed does not alter that chance.

your chance to win via door 1 is also unchanged. still 1/3rd.

now the dilemma. you are given opportunity to switch.

do you keep your 1/3rd chance or do you switch and inherit that 2/3rd chance?