Yesterday’s question looks like a problem about probability, involving maybe a slight inequality in the sex ratio, and maybe failure of independence; but it is not.
The answer is that, among two-child families, it is significantly more likely that the children will be of opposite sex.
As Sune Kristian Jakobsen correctly commented (and also Gordon Royle said to me), the reason given is that parents prefer to have a child of each sex; if their first two are of the same sex, there is a tendency for them to have another. Only those who stop at two are counted in the data.
Thinking about this led me to two speculations. Firstly, I don’t understand this reason. To me, people (including children) are people, and that is that. But if it is true, then a second child of the same sex as his/her older sibling would be slightly unsatisfying to his/her parents. Is there any data about this? Do such children have more problems later in life? (Of course, this would be only a slight tendency; I am certainly not saying that every child in this position would suffer. I am not, in fact, claiming anything.)
The second was to wonder about the evolutionary basis of such a preference, if (as the data seem to show) it exists. Maybe it is true that a child who grows up with a sibling of the opposite sex is less likely to regard the opposite sex as an impenetrable mystery, and so is more successful at choosing a mate. Is there any data about this?
I have no information on either of these points. Anecdotal evidence tells nothing, but careful analysis of large datasets may throw some light.