Mike Speciner speciner@ll.mit.edu said:
It might be that the probability of having same-sex siblings is significantly greater than (or less than) 1/2. In actuality, I suspect it is significantly greater than 1/2. The determination of the gender of a child includes a number of factors that are specific to its parents, including such things as genetics and sexual practices. For example, didn't Henry VIII's wives have some problem with that?
--ms
This brings up a point that has always troubled me a bit. It's challenging to state all of the assumptions required to solve artificial "real-world" word problems. But in my view, stating these assumptions should be left to the problem solver, and not the problem poser. Problems would be too dry if every such problem clearly stated every assumption. It's best to leave it to the reader to make some reasonable assumptions for the purpose of fleshing out an otherwise underspecified problem. While only the most sophisticated of solvers will correctly identify these assumptions, a good solution should include them. In the case of this problem, I don't think it's unreasonable to make the usual (if inaccurate) assumptions even if not all surviving births are independently XX or XY with 50-50 probability. But Mike is dead-on in pointing out that a complete solution explicitly includes these assumptions.