More on the Four-Child Family Problem

Tom Siegler in Charlotte, North Carolina, writes:

I disagree with your reply to the question about the most common distribution of boys and girls in a four-child family. (November 8, 2015) Birth order isn’t relevant. Five combinations are possible: (1) BBBB (2) BBBG (3) BBGG (4) BGGG (5) GGGG. That makes the chances of having three children of one sex (and one of the other) 2 out 5, or 40 percent. The other combinations are all 20 percent.

Marilyn responds:

The original answer is correct. The question was not, “What percentage of the possible combinations of sexes in a four-child family are two of each sex?” It was, “Among parents with four children, what is the most common distribution of boys and girls?” Those questions are different. The answer to the latter refers to how often the various possible combinations actually occur. This is the reason I noted the birth order. It shows why some combinations occur more often than other combinations.