Q.38. A and B are independent events with P(A) = \frac{1}{4} and P(A \cup B) = 2P(B) - P(A), then P(B) is
A. \frac{1}{4}
B. \frac{3}{5}
C. \frac{2}{3}
D. \frac{2}{5}
Answer :- D. \frac{2}{5}
Explanation :-
\begin{aligned} &P(A \cup B) = 2P(B) - P(A) \\ &P(A) + P(B) - P(A \cap B) = 2P(B) - P(A) \\ &P(A) + P(B) - P(B) = 2P(B) - P(A) \\ &\text{[Since A and B are independent events]} \\ &P(B) + P(A) \cdot P(B) = 2P(B) - P(A) \\ &P(B) = \frac{2P(A)}{(1+P(A))} = \frac{2 \times \frac{1}{4}}{\left(1+\frac{1}{4}\right)} = \frac{2}{5} \end{aligned}