Question

A pair has two children. If one of them is boy, then the probability that other is also a boy is

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $\frac{1}{3}$
• D. None of these.

Answer 1

The correct option is C

$\frac{1}{3}$

Explanation for correct option:

Finding probability that other child is boy.

A pair has two child and one is boy

Cases:[(Boy, Boy),(Boy, Girl),(Girl, Boy)]$=3$.

Therefore, if one child is a boy then the no. of favorable cases where the other child will be also a boy: [(Boy, Boy)] $=1$.

Therefore, the probability that the other one is also a boy is

$$\begin{gathered} \mathbf{=}\frac{\mathrm{No}.\mathrm{of}\mathrm{favourable}\mathrm{case}}{\mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{cases}} \\ =\frac{1}{3} \end{gathered}$$

Hence, Option(C) is the correct answer.