this post was submitted on 03 Dec 2023
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I tried to answer but idk why Lemmy failed to post it, so I'll make a tldr instead.
TLDR:
Instead of reasoning I used actual statistics equations and you are correct: the chance in the coins case is 1/3.
However, I was misguided assuming that both the "girl and boy" problem and "coins" problem are the same, when in fact they are not.
In the "coins" case, the statement "at least one of them is heads" has a probability of 3/4. In the "girl and boy" case, the statement "the child that opened the door was a boy" has a probability of 1/2.