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> My brain still wants to short circuit to two doors, one prize, random selection, 50% chance. This seems to be a wide-spread belief/bias ... if there are two choices, two options, two outcomes, then it's 50:50. OK, I buy a lottery ticket ... either I win or I lose, so it's 50:50, right? Of course not. If you can start to see, by default, that two options are not usually equally likely, then you start to lose this misconception. But really, you always have this situation: the prize is behind the door you chose, or it's behind one of the other two. That always remains true, so your probability of having the prize is always 1/3, even if you get to see behind one of the other doors. You're still sticking with your original choice, or switching to both the other doors (although one of them is open, so you ignore it). |