Explanation
We are given:
"A family with three children."
We are required to determine the probability of having three boys in a family with three children.
We can achieve this by getting the probability tree as follows:
We know that probability is given as:
[tex]\begin{gathered} Prob.=\frac{Number\text{ }of\text{ }required\text{ }outcome}{Number\text{ }of\text{ }possible\text{ }or\text{ }total\text{ }outcome}=\frac{n(E)}{n(S)} \\ where \\ E=\lbrace BBB\rbrace;\text{ }n(E)=1 \\ S=\lbrace BBB,BBG,BGB,BGG,GBB,GBG,GGB,GGG\rbrace;\text{ }n(S)=8 \\ \therefore Prob.=\frac{1}{8} \end{gathered}[/tex]Hence, the probability is:
[tex]\operatorname{\therefore}Prob.=\frac{1}{8}[/tex]
