Here is a question you might like to ponder. Answer tomorrow, hopefully.

There exists a large database (I think, held by the American Statistical Association) of information on two-child families. The question is,

Are there more families with the two children of the same sex, or with the two children of opposite sex?

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## About Peter Cameron

I count all the things that need to be counted.

FF, MF, FM, or MM, in other words, the same number of matching sexes as of non-matching sexes. Unless you count hermaphrodites as, say, all the same sex, the answer is just too easy — so what am I missing here?

Oh, right, identical twins. So, there should be more of the same sex than of different!

More of different sexes than of same sex. If two parents have two children of the same sex, they are more likely to get a third child, and be removed from the database.

On the other hand, if we look at the two firstborns in all families with more at least two children, there should be more families where the children are of the same sex: Boys are slightly more common than girls, and the probability that the two children have different sexes, 2p(1-p), is <½ when p != ½.

Agree with SKJ on both counts. In the second case, you’d also expect positive correlations between sexes of the children due to genetic and environmental factors. No idea how strong such an effect is though! Does the data cover multi-child families or just 2-child?