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 17 and that of B is 29 . Find the probability that both of them are selected.

Answer: Option C

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:
$$\begin{array}{rl}& =\left(\frac{1}{7}\right)\times \left(\frac{2}{9}\right)\\ & =\frac{2}{63}\end{array}$$