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If the gender of a child were an independent variable then the genders of the existing children would be irrelevant and so the probability of the next child being a girl would be approximately 1/2.

It would be approximately 1/2 because the overall proportion is not exactly half. However, and more important, is the fact that the gender of a child is affected by the parents' genes and so is not independent of the gender of previous children.

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Q: When a family of seven boys and no girls is expecting an eighth child what is the probability of the next child being a girl?
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