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An intuitive explanation is that, if the contestant initially picks a goat (2 of 3 doors), the contestant will win the car by switching because the other goat can no longer be picked – the host had to reveal its location – whereas if the contestant initially picks the car (1 of 3 doors), the contestant will not win the car by switching. [12]
Exactly as above, if the host always reveals a goat, then we get no information about whether there were originally two goats, or one goat and one car, because the host always reveals a goat, regardless. So the probability that there were a car and a goat behind the two unchosen doors remains 2/3.
When you choose a door with a goat (2/3 odds), Monty must show you the other goat, so the car will be behind the door you didn't pick. So 2/3 of the time, switching will get you the car. Here's another way to put it: you win if you pick a goat and then switch. The odds of picking a goat are 2/3, so if you always switch you win 2/3 of the time.
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Mathematically, the problem shows that a player switching to the other door has a 2 ⁄ 3 chance of winning under standard conditions, but this is a counterintuitive effect of switching one's choice of doors, and the problem gained wide attention due to conflicting views following vos Savant's publication, with many asserting that the ...
Also, at one point, Mark and Helly wander down the labyrinth of brightly-lit, indistinguishable hallways on their floor, open a door, and find a guy feeding milk to baby goats.
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