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> I don't think you even need P(W = 0) = P(W = 1) = 0.5.

You do,

In the article, the prior of interest is the prior gender of a child, which can be safely assumed to be 0.5. Similarly, independence of children's genders is a very good approximation as well. It wasn't necessary for the article to state these assumptions because they are obvious common knowledge.



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