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Suppose you’re on a game show, and you’re given the choice of five doors: Behind one door is a car; behind the others, goats. You pick a door, and then the host, opens two of the doors, which guaranteed have goats. He then says to you, “Do you want to switch to other door?” What is the probability of winning if you decide to switch

Ritu
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    Switch to which door? If you've picked one door and the host opens two of the doors, that leaves two doors to switch to. – Kman3 Aug 31 '20 at 19:58

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Each door that can be switched too has a $2/5$ chance have having the car, while your original door only has a $1/5$ chance.

This can be seen as there is a $4/5$ chance you choose wrong at first, so there is a $4/5$ chance it is in one of the two of the doors that can be switched too. It is also clear they have the same chance of being correct, so it must be a $2/5$ chance.

Physical Mathematics
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