One of the famous intuitive mistakes in probability comes from the simple question, "Do boys have more sisters than girls do?" A quick analysis of the situation may prompt you to say yes. A more in-depth look might change your mind.

I don't have a sister. I have to say, I don't feel much deprived, except when I think of the millions I might make if I were to get my sister to drive across America with me, or volunteer in Bangladesh with me, or meditate with me every morning for a year, and then write a sappy best-selling memoir about it. The question is, did being born female decrease my odds of having a sister?

This is the set-up for a well-known question in probability. A quick look at the idea might give you the impression that, yes, boys have more sisters than girls do. A two-child family that includes a boy and a girl gives the boy a sister, and the girl a nothing but a contemptible brother. Even if the parents had another child, and provided their daughter with a sister, the boy would now have two sisters to the girl's one. Boys have the advantage, it seems.

Or do they? Let's look at the cases one by one. A two-child family can have four different combinations, two girls, an elder girl and a younger boy, an elder boy and a younger girl, and two boys. The families with two children of the same sex provide no sisters to any boy, but one sister to each of the two girls - making for two girls with two sisters. The families with one boy and one girl provide no sisters for the girls, but one sister for each of the two boys - two boys with two sisters. So far each sex is provided with equal amounts of sisters.

How about three-child families? There are three general combinations. A family of three boys yields zero sisters for anyone. A family of three girls nets three separate girls two sisters each, making for six sisters for three girls. So far, six sisters for female children.