<p>If \(C\) and \(D\) are two events such that \(C \subseteq D\) 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 a subset of D, meaning whenever C occurs, D must occur. This fundamental set relationship directly constrains conditional probability: P(C|D) = P(C∩D)/P(D) = P(C)/P(D) since C∩D = C.
<p><strong>Step 1:</strong> Since C ⊆ D, whenever event C occurs, event D must occur. This means C∩D = C (the intersection equals C).</p><p><strong>Step 2:</strong> Apply conditional probability definition: 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), therefore P(C)/P(D) ≤ 1.</p><p><strong>Step 4:</strong> The correct statement is: <strong>P(C|D) = P(C)/P(D)</strong> or equivalently <strong>P(C|D) ≥ P(C)</strong> (since P(D) ≤ 1), or <strong>P(D|C) = 1</strong> (since C∩D = C means D always occurs when C occurs).</p><p>∴ Answer: C</p>
Correct Answer: C