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 need to think about it in terms of the chance you were wrong.
When you pick one of three doors, there’s a 2/3 chance you chose a door without the prize behind it.
The game master then opens one of the doors you didn’t choose, to show you there wasn’t a prize behind it. But this doesn’t tell you anything you didn’t already know – you knew there was only one door with a prize, so at least one of the two you didn’t choose would have to also not have a prize. Your chance of having picked the wrong door is still 2/3, so you should switch, turning that into a 2/3 chance of winning.
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