Probability
Conditional Probability
Grade 12
Question:
<p>A and B are two events such that P(A) > 0, P(B) ≠ 1, then P(B'/A) is equal to</p>
<p>(a) 1 - P(B/A)</p>
<p>(b) 1 - P(A/B)</p>
<p>(c) \(\frac{1 - P(A \cup B)}{P(B)}\)</p>
<p>(d) \(\frac{P(A)}{P(B)}\)</p>
Step-by-Step Solution
Key Concept: Use the complement rule and definition of conditional probability: P(B'/A) = 1 - P(B/A).
<p><strong>Step 1:</strong> By definition, P(B'/A) = P(B' ∩ A)/P(A)</p><p><strong>Step 2:</strong> Note that B' ∩ A = A - B = A - (A ∩ B), so P(B' ∩ A) = P(A) - P(A ∩ B)</p><p><strong>Step 3:</strong> Therefore P(B'/A) = [P(A) - P(A ∩ B)]/P(A) = 1 - P(A ∩ B)/P(A) = 1 - P(B/A)</p><p>∴ Answer is (a)</p>
Correct Answer: A