If $A$ and $B$ are independent events, then which of the following is/are true?
(A) $\bar A$ and $B$ are independent events
(B) $P(A ∩ B) = 0$
(C) $\bar A$ and $\bar B$ are independent events
(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) → (A) and (C) only
Given: A and B are independent events.
(A) Ā and B: This is correct. If two events are independent, then the complement of one event is also independent of the other.
(B) P(A ∩ B) = 0: This is incorrect. For independent events, P(A ∩ B) equals P(A) × P(B), not necessarily 0.
(C) $\bar A$ and $\bar B$ are independent events: This is correct. Complements of independent events are also independent.
(D) P(A ∩ B) = P(A) + P(B):This is incorrect. The correct relation is: P(A ∩ B) = P(A) × P(B)