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
Let’s pretend that instead of opening a door and showing you a goat, Monty just says, “Hey, instead of the *one* door you already picked…you can switch to the other *two* doors.”
Clearly two doors gives you better odds of winning than one door does. Specifically 2/3 chance.
And of those two other doors…one of them definitely has a goat behind it (because there is only one winning door)
So ask yourself…..why would opening that door and showing the goat change those odds?
The answer, of course, is that it doesn’t…. which is why you should always switch.
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