Why does the probability “lock in” and not change if you remove a variable but doubles for the other one?
I read it multiple times and it still doesnt make any logical sense to me.
In: Mathematics
You pick a door, let’s just say door 1.
What are the chances you guessed the door with the prize? 1 out of 3.
That means there’s a 2 out of 3 chance you guessed wrong, correct?
So now Monty reveals the prize was not behind door 2.
The chances that you guessed wrong initially *are still* 2 out of 3. By switching, you’re taking the odds that you initially guessed wrong.
Imagine it was 10 doors. You had a 90% chance of guessing the wrong door at the beginning.
Monty opens *eight* of the other doors.
The chance you guessed wrong initially is *still* 90%, and you’re being asked “Do you *really* think you’re *that* lucky to have guessed right? Or is it starting to get suspicious that I, the host of the show who knows where the prize is, haven’t opened this *one* other door?”
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