<p>If \(A\) and \(B\) are two independent events then \(P(A \cap B) + P(A)P(B) = P(A)\).</p>
Step-by-Step Solution
Key Concept: For independent events A and B, P(A∩B) = P(A)·P(B). Substituting this into the given equation and solving reveals a constraint on P(A) or P(B) that determines when the statement is true.
<p><strong>Step 1:</strong> For independent events A and B, we know that P(A∩B) = P(A)·P(B).</p><p><strong>Step 2:</strong> Substitute this into the given equation: P(A)·P(B) + P(A)·P(B) = P(A)</p><p><strong>Step 3:</strong> Simplify: 2P(A)·P(B) = P(A)</p><p><strong>Step 4:</strong> Factor out P(A): P(A)[2P(B) - 1] = 0</p><p><strong>Step 5:</strong> This means either P(A) = 0 or P(B) = 1/2. The statement is NOT generally true for all independent events A and B—it's a conditional relationship. The given statement as a general claim is <strong>FALSE</strong>.</p><p>∴ Answer: B (The statement is false/the equation doesn't hold for arbitrary independent events)</p>
Correct Answer: B