Question

An experiment consists of recording boy-girl composition of families with 2 children. (i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births? (ii) What is the sample space if we are interested in the number of girls in the family?

Answer 1

It is given that each family has 2 children.

(i)

Consider G represents a girl while B represents a boy.

Thus, the sample space in knowing whether it is a boy or a girl in the order of their births is,

S={ GG,GB,BG,BB } .

(ii)

As it is given that each family consists of 2 children, there can be a possibility that both are girls, or one is girl and other is boy, or both are boys and no girls.

Thus, the sample space in knowing the number of girls in a family is,

S={ 0,1,2 } .