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
Because switching doors is guaranteed to switch whether or not you have the prize. If your chosen door had the prize, Monty will open one of the goat doors at random, leaving one goat door for you to switch to. If you chosen door had a goat, Monty will open the other goat door, leaving only the prize door for you to switch to.
Because you had a 1/3 chance of picking the prize door at the beginning, and switching doors is guaranteed to switch whether or not you have the prize, then switching turns the chances of winning from 1/3 to 2/3.
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