Question

Calculate the probability of having three boys in a family with three children. You may make a list or make a tree diagram.

Answer 1

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:

`\begin{gathered} Prob.=\frac{Number\text{ }of\text{ }required\text{ }outcome}{Number\text{ }of\text{ }possible\text{ }or\text{ }total\text{ }outcome}=(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.=(1)/(8) \end{gathered}`

Hence, the probability is: