## More Sisters on Average

Who have more sisters on average in a society: boys, girls, or is it equal?

*Remark: Assume that each child is born a boy or a girl with equal probability, independent of its siblings.*

**SOLUTION**

The average number of sisters is roughly the same for both boys and girls. To see this, notice that every girl in every family contributes “one sister” to each of its siblings who are either a boy or a girl with equal probability. Therefore, every girl contributes on average the same number of sisters to the group of boys and to the group of girls. Since there is roughly the same number of boys and girls in the society, the average number of sisters for boys and girls is the same.