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(A) In an experiment with $2$ children,each child can be either a boy $(B)$ or a girl $(G)$.Since we are interested in the order of birth,we consider

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$S = \{ BB, BG, GB, GG \}$

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(A) In an experiment with $2$ children,each child can be either a boy $(B)$ or a girl $(G)$.Since we are interested in the order of birth,we consider all possible sequences of length $2$.The possible outcomes are:$1$. First child is a boy,second is a boy: $BB$$2$. First child is a boy,second is a girl: $BG$$3$. First child is a girl,second is a boy: $GB$$4$. First child is a girl,second is a girl: $GG$Therefore,the sample space $S$ is given by $S = \{ BB, BG, GB, GG \}$.

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

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