Assuming random chance and a 50% probability of having a girl baby, the probability of that happening is less than .2% The actual probability is somewhat lower, just under .1% because actual probabily of a girl baby is 48.78%. (About 1.05 boy badies per girl baby).
I'd say the Imperial family has a problem making sperm with Y chromosomes.
Very interesting discussion. I will have to come back to it to see where it goes.