Question

$X$ has three children in his family. What is the probability that all the three children are boys?

• A. $\frac{1}{8}$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{3}{8}$

Answer 1

The correct option is A $\frac{1}{8}$

X has $3$ children in his family.

All possible outcomes are if $G$ represents girl child and B represent boy child, $\left\{\right(BBB),(BBG),(BGB),(BGG),(GBB),(GBG),(GGB),(GGG\left)\right\}$, hence $n\left(S\right)=8$

Out of which favorable outcomes for all the three chilren being boy, $n\left(E\right)=1$

Hence, the probability that all the three children are boys is $\frac{n\left(E\right)}{n\left(S\right)}=\frac{1}{8}$