If A and B are two independent events, then which of the following is/are true?
(A) $P(A∩B) = 0$
(B) $P(A∪B) = 1-P(A') P(B')$
(C) $P(A∪B) = P(A) P(B)$
(D) $P(A∩B) = P(A) P(B)$
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (B) and (D) only **
Given: A and B are independent events.
(A) $P(A \cap B)=0$ False — independence does NOT imply probability of intersection is zero.
(B) $P(A \cup B) = 1 - P(A')P(B')$ True — for independent events, $P(A' \cap B') = P(A')P(B')$ and $P(A \cup B)=1-P(A' \cap B')$.
(C) $P(A \cup B)=P(A)P(B)$ False — this is the probability of intersection, not union.
(D) $P(A \cap B)=P(A)P(B)$ True — definition of independence.
Correct statements: (B) and (D).