<p>If A and B are two mutually exclusive events, then</p>
Step-by-Step Solution
Key Concept: Mutually exclusive events cannot occur simultaneously, so their intersection is empty (P(A ∩ B) = 0) and P(A ∪ B) = P(A) + P(B). This is fundamentally different from independent events.
<p><strong>Step 1:</strong> Recall that mutually exclusive (or disjoint) events cannot occur at the same time.</p><p><strong>Step 2:</strong> By definition, if A and B are mutually exclusive, then A ∩ B = ∅ (empty set).</p><p><strong>Step 3:</strong> Therefore: P(A ∩ B) = 0</p><p><strong>Step 4:</strong> The probability of their union is: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = P(A) + P(B)</p><p><strong>Step 5:</strong> Common statements for mutually exclusive events:</p><ul><li>P(A ∩ B) = 0 ✓</li><li>P(A ∪ B) = P(A) + P(B) ✓</li><li>P(A|B) = 0 (if P(B) ≠ 0) ✓</li><li>They cannot both occur in a single trial ✓</li></ul><p>∴ Answer: A</p>
Correct Answer: A