There are two children in a family.

The probability that both of them are boys is

The correct option is C

$\frac{1}{4}$

Explanation for the correct answer:

Compute the required probability:

Let “$B$” represent the boy and “$G$” represent the girl

The sample space is listed as

$S=\left\{BB,BG,GB,GG\right\}$

The event where both the children are boys is

$A=\left\{BB\right\}$

The probability of event $A$ is

$p\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{1}{4}$

Hence, there is $\frac{1}{4}$ possibility of both children being boys in a family having two children.

Hence, option $\left(C\right)$ is the correct answer.