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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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You can't just end the experiment if the randomly chosen child doesn't "fit the parameters", by doing that you aren't accounting for half the girls in the whole event pool. Half of the girls have siblings that are girls.
Being 2 girls was a possible event at the start, you can't just remove it. This time it happened to be a boy who opened the door, but it could've been as likely for a girl to open it.
If it was phrased like "there are 2 siblings, only boys can open doors. Of all the houses that opened their doors, how many have a girl in them?", then it will be 2/3. In this example, there is an initial pool of events, then I narrowed down to a smaller one (with less probability). If you "just" eliminate the GG scenario, then the set of events got smaller without reducing the set's probability.
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.