Right, assuming not too many families stop at one if and only if the first is a boy - that would throw off 2. Note 2': among all girls who are the eldest or second eldest child, the other sibling will be a brother in about half the cases; in contrast with 3: among all families with at least two children, with at least one of the older two being a girl, one-third have two girls. The difference is that 2' double counts families with two girls - once for each girl. Franklin T. Adams-Watters -----Original Message----- From: David Gale <gale@math.berkeley.edu> Ok, here's a concrete proposal. Chose a city with at least 50,000 inhabitants, say Dubuque, Iowa, population 57,686. Get access to census data. I predict 1.Among all families having at lest two children the two eldest will have opposite sexes in about half the cases. 2. Among all Mary's who are the eldest or second eldest child, the other sibling will be a brother in about half the cases.