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The question cannot be answered properly because the children's genders are not independent events. They depend on the parents' ages and their genes. Furthermore, it is often wrongly assumed that the probability of a boy is 50%. That is simply not true: the latest information shows that the probability of a boy is 52%.

However, if you choose to ignore reality then the solution, based on the Binomial(9, 1/2) distribution, is that the probability is 0.1641, approximately.

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10y ago

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Q: What is the probability of having 6 boys and three girls?
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