I am studying probability, and one of the lectures I came across (Skip to 52:00) states that the sex of siblings is not mutually independent and that there is some correlation.
Can anyone tell me why? And if so, where is the evidence?
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There is at least one paper that claims this:
A test for heritability of the sex ratio in human genealogical data is reported here, with the finding that there is significant heritability of the parental sex ratio by male, but not female offspring.
--Trends in Population Sex Ratios May be Explained by Changes in the Frequencies of Polymorphic Alleles of a Sex Ratio Gene. Corry Gellatly, Evolutionary Biology 36:190-200, 2009 DOI: 10.1007/s11692-008-9046-3.
In other words (simplistically) some families are more prone to have male offspring, which implies that the probability of male offspring is not independent. However, this is a hypothesis, not a proven fact, and I think it's not a very strong hypothesis.
A non-scholarly, but apparently careful, discussion is here:
The odds of having a girl seem decrease after having each boy, but only very slightly. Even after 3 boys, you are only 6.4% more likely to have a 4th boy than a girl.