Two brother X and Y appeared for an exam. Let A be the event that X is selected and B is the event that Y is selected.
The probability of A is $$\frac{{1}}{{7}}$$ and that of B is $$\frac{{2}}{{9}}$$. Find the probability that both of them are selected.

A. $$\frac{{1}}{{63}}$$

B. $$\frac{{2}}{{35}}$$

C. $$\frac{{2}}{{63}}$$

D. $$\frac{{9}}{{14}}$$

Answer: Option C

Solution(By Examveda Team)

Given, A be the event that X is selected and B is the event that Y is selected.
$$P(A) = \frac{1}{7},\,P(B) = \frac{2}{9}$$
Let C be the event that both are selected.
P(C) = P(A) × P(B) as A and B are independent events:
$$\eqalign{ & = \left( {\frac{1}{7}} \right) \times \left( {\frac{2}{9}} \right) \cr & = \frac{2}{{63}} \cr} $$