<p>If C and D are two events such that \(C \subset D\) and \(P(D) \neq 0\), then the correct statement among the following is</p>
Step-by-Step Solution
Key Concept: When C ⊂ D, event C is contained within D, so whenever C occurs, D must occur. This means P(C ∩ D) = P(C), and the conditional probability P(C|D) = P(C)/P(D) ≥ P(C) since P(D) ≤ 1.
<p><strong>Step 1:</strong> Since C ⊂ D, every outcome in C is also in D. Therefore, C ∩ D = C.</p><p><strong>Step 2:</strong> By definition of conditional probability: P(C|D) = P(C ∩ D)/P(D) = P(C)/P(D)</p><p><strong>Step 3:</strong> Since C ⊂ D, we have P(C) ≤ P(D). With P(D) ≠ 0, dividing by P(D) gives: P(C|D) = P(C)/P(D) ≥ P(C)</p><p><strong>Step 4:</strong> Also, since P(D) ≠ 0 and C ⊂ D, we have P(C|D) ≤ 1 and P(C|D) = 1 only when C = D.</p><p><strong>Step 5:</strong> The correct statement is: <strong>P(C|D) ≥ P(C)</strong> and <strong>P(C|D) = P(C)/P(D)</strong></p><p>∴ Answer: A</p>
Correct Answer: A