response 112 of 132:

Sep 4 17:42 UTC 1997

Another way to find the expected number of girls G (which doesn't require
any calculus) is: 

         G = 0/4 + 1/4 + 1/4 + 2/8 + 3/16 + 4/32 + ...
           = 1/4 +       1/4 + 2/8 + 3/16 + 4/32 + ...
==>     2G = 2/4 + 1/2 + 2/4 + 3/8 + 4/16 + 5/32 + ...
==>   2G-G = 1/4 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ...
==>      G = 1/4 + (1/2)/(1-1/2)
           = 1/4 + 1
           = 5/4

Drew's interesting observation about the increase in population is quite
right, each generation will be 25% bigger than the last if everyone has
children.  That would be kind of a problem.