Game One: You are given a choice of three doors. You pick number one. The host opens one of the other two doors, having been given instructions that, if you pick the car, the host is to open one of the other doors, and if you pick a goat, the host opens the other door with a goat. Stalemate. It is a predetermined outcome.
Game Two: The prior game’s outcome stands. The new choice you have is do you keep door number one, or do you switch?
How do you have a 2/3 chance of winning if you switch?
In: 107
Imagine this game, but with a different phrasing.
You pick one door at random. So you have a 1/3 chance of picking the car.
The host points to one of the other two doors, and says “the car is in here”. If you accidentally picked the car (1/3 chance), they are lying to you. If you picked a goat (2/3 chance), they have to tell the truth.
Statistically, this game is identical. Since the host is not allowed pick the car, they are suggesting semi-honestly that the door they keep closed is the one with the car.
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