### Law of Large Numbers Failed

Problem: There are two maternity hospitals in a town with 50 and 500 beds. Given full occupancy on a particular day, which of these hospitals is more likely to have equal no of boys and girls given probability of boys = probability of girls ? What would the answer intuitively be by #LawOfLargeNumbers? You would see #LawOfLargeNumbers does not seem to work here. How should the statement be positioned for #LawOfLargeNumbers to work?