If A and B are two events defined on a sample space with the probabilities P A = 0.5 , P B = 0.69 and P A B = 0.5 , then the value of P A A c ∪ B c is equal to

Question

If A and B are two events defined on a sample space with the probabilities P A = 0.5 , P B = 0.69 and P A B = 0.5 , then the value of P A A c ∪ B c is equal to, 2 5, 3 13, 31 131, 100 131

MARKS App · Accepted Answer

P A B = P A ∩ B P B = 0.5 ⇒ P A ∩ B = 0.5 × 0.69 = 0.345 P A A c ∪ B c = P A ∩ A c ∪ B c P A c ∪ B c = P A ∩ B c P A ∩ B c = P A - P A ∩ B 1 - P A ∩ B = 0.5 - 0.345 1 - 0.345 = 0.155 0.655 = 31 131

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