Firstly, I do apologize if the subject of this email would have been better in a forum but seeing as it is an observation on one of your problems, rather than a question I thought you might be interested. If not stop reading now!
The problem in question is Family Statistics.
I read this problem and was a typical reader, initially I thought that there would be more boys with sisters and then realized, when it was pointed out, that the 'all girls' families would not supply any boys with sisters but all the girls would have sisters. It was not apparent to me intuitively that the 'all girls' situation would exactly balance the mixed families but I scanned the maths and was prepared to accept it (as I still am).
Now the interesting bit:
Being quite impressed with this problem I posed the question "Do men have more sisters than women?" to a colleague at work who had a quick think and replied "No, they have the same." I immediately assumed he had misunderstood the question and explained why you 'should' expect more men to have sisters i.e. in a mixed family the girls have one less sister. To which he replied, "Forget that. For any one person (gender unspecified) the gender distribution of their siblings is un affected by their own gender. There are the same number of men and women to be that one person. Therefore men and women have the same number of sisters."
I was initially not convinced by this line of reasoning because it seems too simple and also it reminds me of what you call the Bear cubs problem, so I assumed that he was right but for the wrong reasons. I also wanted him to acknowledge that the gender of the 'one person' affects the number of sisters. However, after much reflection I have to concede that he is right for the right reasons.
Copyright © 1996-2018 Alexander Bogomolny