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
There doors, one of them has the prize. The host will open an empty door once you pick one. Then you can either switch to the other or go with your first choice.
When do you win if you don’t switch? When your first choice was right. Thats 1 out of 3 so the probability of you winning is ⅓.
When do you win when you switch? When your first choice was wrong, because if thats the case you can only switch to the winning door. Your first choice is wrong 2 out of 3 times so the probability of you winning with switching is ⅔.
With no switching you only win when your first choice was right (⅓) and with switching you only win when your first choice was wrong (⅔).
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