<p>The probability of \(A\) occurring is 0.5 and of \(B\) occurring is 0.3. If \(A\) and \(B\) are mutually exclusive events then the probability of neither \(A\) nor \(B\) occurring is</p>
Step-by-Step Solution
Key Concept: For mutually exclusive events, use P(A ∪ B) = P(A) + P(B), then P(neither A nor B) = 1 - P(A ∪ B) using the complement rule.
<p><strong>Step 1:</strong> Since A and B are mutually exclusive, P(A ∩ B) = 0</p><p><strong>Step 2:</strong> Find P(A ∪ B) using the addition rule: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.5 + 0.3 - 0 = 0.8</p><p><strong>Step 3:</strong> Probability of neither A nor B occurring = P(A' ∩ B') = P((A ∪ B)') = 1 - P(A ∪ B) = 1 - 0.8 = 0.2</p><p>∴ Answer: D (0.2)</p>
Correct Answer: D