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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?

Solution
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When there are 2 children in a family, they can be both boys , both girls or 1 boy and 1 girl
(i) When the order of the birth of a girl or a boy is considered the sample space is given by S={GG,GB,BG,BB}
(ii) Since the maximum number of children in each family is 2, a family can either have 2 girls or 1 girl or no girl. Hence the required sample space is S={0,1,2}

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