David Gale wrote:
2. Pick a girl at random. Then the odds are even that she has a brother, (because there are (roughly) the same number of girls with brothers as there are girls with sisters).
Do you mean "pick a girl at random from a two-child family?
PS. Are there really twice as many boy-girl families as girl-girl or boy-boy? It shouldn't be too hard to check. Maybe certain couples are biologically more likely to produce one sex over the other.
With mostly anecdotal evidence, there are many families that follow the following strategy as long as they are able: (1) have a child (2) if all children are the same gender, goto 1 (3) done or with the alternative: (2)' if all children are female, goto 1 With either strategy, it is much more likely than 1/2 that a two-child family has one of each gender. --ms