Question

A parents 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 $\frac{1}{3}$

Total cases are $BB,BG,GB,GG=4$
Favorable cases are $BB,BG,GB=3$
Let $P\left(A\right)=$ Probability of a boy in two children
$=\frac{3}{4}$
The probability that the second child is also a boy is $P(A\cap B)=\frac{1}{4}$
We have to find $P\left(\frac{B}{A}\right)=\frac{P(A\cap B)}{P\left(A\right)}=\frac{\frac{1}{4}}{\frac{3}{4}}=\frac{1}{3}$