<p>A die is thrown. Let <em>A</em> be the event that the number obtained is greater than 3. Let <em>B</em> be the event that the number obtained is less than 5. Then \(P(A \cup B)\) is</p>
Step-by-Step Solution
Key Concept: Find A and B as subsets of sample space, then use P(A ∪ B) = P(A) + P(B) - P(A ∩ B) to avoid double-counting the intersection.
<p><strong>Step 1:</strong> Identify event A (number > 3): A = {4, 5, 6}, so P(A) = 3/6 = 1/2</p><p><strong>Step 2:</strong> Identify event B (number < 5): B = {1, 2, 3, 4}, so P(B) = 4/6 = 2/3</p><p><strong>Step 3:</strong> Find intersection A ∩ B (number > 3 AND < 5): A ∩ B = {4}, so P(A ∩ B) = 1/6</p><p><strong>Step 4:</strong> Apply union formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 1/2 + 2/3 - 1/6 = 3/6 + 4/6 - 1/6 = 6/6 = 1</p><p>∴ Answer: C (P(A ∪ B) = 1)</p>
Correct Answer: C