<p>The probability that at least one of the events \(A\) and \(B\) occurs is 0.60. If \(A\) and \(B\) occur simultaneously with probability 0.20 then \(P(A') + P(B')\) is equal to</p>
Step-by-Step Solution
Key Concept: Use the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B) to find P(A) + P(B), then calculate P(A') + P(B') = 2 - [P(A) + P(B)].
<p><strong>Step 1:</strong> Given information:</p><p>• P(A ∪ B) = 0.60 (at least one event occurs)</p><p>• P(A ∩ B) = 0.20 (both events occur simultaneously)</p><p><strong>Step 2:</strong> Use the addition rule:</p><p>P(A ∪ B) = P(A) + P(B) - P(A ∩ B)</p><p>0.60 = P(A) + P(B) - 0.20</p><p>P(A) + P(B) = 0.80</p><p><strong>Step 3:</strong> Calculate P(A') + P(B'):</p><p>P(A') + P(B') = [1 - P(A)] + [1 - P(B)]</p><p>P(A') + P(B') = 2 - [P(A) + P(B)]</p><p>P(A') + P(B') = 2 - 0.80 = 1.20</p><p><strong>∴ Answer: 1.20</strong></p>
Correct Answer: C