If A and B are independent events with P(A) = 0.3 and P(B) = 0.6, then \(P(A\cup B)\) is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0.72
For independent events, \(P(A\cap B) = P(A)\,P(B)\):
\(P(A\cap B) = 0.3\times 0.6 = 0.18\)
By the addition theorem:
\(P(A\cup B) = P(A)+P(B)-P(A\cap B)\)
\(P(A\cup B) = 0.3+0.6-0.18 = 0.72\)
Why the other options are incorrect
Option (1) 0.9 — Incorrect. This is P(A) + P(B), which counts the common part twice; that works only for mutually exclusive events.
Option (2) 0.18 — Incorrect. This is \(P(A\cap B)\), not \(P(A\cup B)\).
Option (4) 0.28 — Incorrect. This is \(P(A')P(B') = 0.7\times 0.4\), the probability that neither event happens.