Probability
Addition Theorem of Probability
Grade 12
Question:
<p>If \(P(A) = 0.8\), \(P(B) = 0.5\), and \(P(B/A) = 0.4\), find \(P(A \cup B)\).</p>
<p>\(0.80\)</p>
<p>\(0.90\)</p>
<p>\(0.98\)</p>
<p>\(1.00\)</p>
Step-by-Step Solution
Key Concept: Use the conditional probability formula P(B|A) = P(A∩B)/P(A) to find P(A∩B), then apply P(A∪B) = P(A) + P(B) - P(A∩B).
<p><strong>Step 1:</strong> Find P(A∩B) using conditional probability.</p><p>Given: P(B|A) = 0.4, so 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> Apply the addition rule for probability.</p><p>P(A∪B) = P(A) + P(B) - P(A∩B)</p><p>P(A∪B) = 0.8 + 0.5 - 0.32</p><p>P(A∪B) = 1.3 - 0.32 = 0.98</p><p>∴ Answer: C (0.98)</p>
Correct Answer: C