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
The important piece of information is that the host knows the correct answer. They aren’t picking randomly.
Your first choice is 1/3 to be correct, 2/3 to be wrong.
Then the host removes one of the incorrect answers.
Your first choice is still 2/3 chance to be wrong. But now there is only one other choice, so logically it must be 1/3 to be wrong, or 2/3 to be correct.
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