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Glitch in the matrix
(ani.social)
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this post was submitted on 03 Dec 2023
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It depends on what you classify as the "start". If all households with two children everywhere? Sure. But the story explicitly starts with us knowing a boy came to the door. By the parameters of the story, we know that's what happened.
We don't just eliminate GG, we also eliminate any BG or GB where it just so happened that the girl came to the door. Because that's what we already know is true, and we're asking for the conditional probability given that this has already happened.
You didn't eliminate BG and GB where a girl opens the door though. If you do that, then the answer is 50%. Because you remove half the probability from BG and GB and you remove none from BB.
I know you didn't eliminate those cases because you said "That leaves us with 3 possibilities with equal probabilities". That would be false, BB is twice as likely.
I'm guessing you haven't read the rest of the thread? My first comment was incorrect and the correction has been made.