Given that A and B are mutually exclusive events.
We know that,
When two events are mutually exclusive, then
P(A ⋂ B) = 0
By General Addition Rule:
P(A ⋃ B) = P(A) + P(B) – P(A ⋂ B)
⇒ P(A ⋃ B) = P(A) + P(B) – 0
⇒ P(A ⋃ B) = P(A) + P(B)
We know that, for all events A, B
0 ≤ P(A) ≤ 1
∴ P(A) + P(B) ≤ 1
⇒ P(A) ≤ 1 – P(B)
[By complement rule]
Hence, the correct option is (A).
