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:

(A) and (C) only

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)