Probability
Conditional Probability
Grade None
Question:
<p>If \(P(A) = 0.8\), \(P(B) = 0.5\), and \(P(B/A) = 0.4\), find \(P(A/B)\).</p>
<p>\(0.32\)</p>
<p>\(0.40\)</p>
<p>\(0.64\)</p>
<p>\(0.80\)</p>
Step-by-Step Solution
Key Concept: Use the conditional probability formula P(A/B) = P(A∩B)/P(B), where P(A∩B) can be found from P(B/A) = P(A∩B)/P(A). Chain these relationships to solve for P(A/B).
<p><strong>Step 1:</strong> Find P(A∩B) using the definition of P(B/A).</p><p>Given: P(B/A) = P(A∩B)/P(A)</p><p>0.4 = P(A∩B)/0.8</p><p>P(A∩B) = 0.4 × 0.8 = 0.32</p><p><strong>Step 2:</strong> Use P(A/B) = P(A∩B)/P(B).</p><p>P(A/B) = 0.32/0.5 = 0.64</p><p>∴ Answer: C (0.64)</p>
Correct Answer: C