Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Probability Distributions

Question:

A family has two children, the probability that both the children are boys, if given that at least one of them is a boy is :

Options:

$\frac{2}{3}$

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{3}{4}$

Correct Answer:

$\frac{1}{3}$

Explanation:

The correct answer is Option (3) → $\frac{1}{3}$

$\text{P (Both Boys | At least one boy)=P(A|B)}$

$P(A|B)=\frac{P(A∩B)}{P(B)}=\frac{\frac{1}{4}}{\frac{3}{4}}=\frac{1}{3}$