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
Perhaps the best way to think of probability is in terms of information. If two phenomenon are independent, what that really means is that one doesn’t give you any information about the other.
So now let’s consider the doors. You pick a door and Monty then gives you a bit of information you didn’t have before: one of the two doors the prize isn’t behind.
Since you have more information in the ‘second game’ than the ‘first game’, they cannot be independent of one another. That information must *somehow* alter your odds.
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