## 2. As many boys as girls

Consider all possible families with two children. Half of such families are "lucky," i.e., the number of boys in the family matches the number of girls. Is the same true for families with four children? (Assume that the birth of a boy and a girl is equally likely.)
2. We will call the "distribution" of children in a family a sequence of four children characterized only by their gender and listed in order of seniority. For example: "boy, girl, boy, boy," which we will briefly write as "BGBB".

Families with four children correspond to 16 types of equally probable distributions:

BBBB; BBBG; BBGB; BGBB; GBBB; BBGG; BGBG; BGGB; GBBG; GBGB;

GGBB; BGGG; GGBB; GGBG; GGGB; GGGG.

Six of these 16 types of distributions correspond to an equal number of boys and girls, so the probability of a "successful" family is $6 / 16 = 3 / 8$.

This value differs from the value $1 / 2$, which was obtained in the case of families with two children.