Question

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

• A. $\frac{1}{8}$
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. $\frac{3}{8}$

Answer 1

Answer: (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, $\left(BBB\right),\left(BBG\right),\left(BGB\right),\left(BGG\right),\left(GBB\right),\left(GBG\right),\left(GGB\right),\left(GGG\right),$ hence $n\left(S\right)=8$

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

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