Question

Probability of birth of a girl or a boy child is equally likely. If a family has two children and it is known that the youngest child is a girl , then the probability that both the child born are girls is

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

Answer 1

The correct option is B $\frac{1}{2}$

If B represents boy and G represents girl then,
Sample space will be $\{BB,GB,BG,GG\}$
$\therefore$ The required probability $=\frac{1}{2}$
Alternate solution
one child is given as a girl child and $P\left(G\right)=P\left(B\right)=\frac{1}{2}$
$\therefore$ The probability that the other child is also a girl is $\frac{1}{2}$