Question

A parent has two children. If one of them is a boy, then the probability that the 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 the correct option:

To find the required probability:

Total cases are BB, BG, GB, GG $=4$

Favorable cases are BB, BG, GB $=3$

Let $P\left(A\right)=$the Probability of a boy in two children

$=\frac{3}{4}$

The probability that the second child is also a boy is $P\left(A\cap B\right)=\frac{1}{4}$ (favorable case BB)

We have to find $P\left(\frac{B}{A}\right)=\frac{P\left(A\cap B\right)}{P\left(A\right)}=\frac{{\displaystyle \frac{1}{4}}}{{\displaystyle \frac{3}{4}}}=\frac{1}{3}$

Hence ,the correct option is (C).