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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

Options

  1. A2 5
  2. B3 13
  3. C31 131
  4. D100 131

Correct answer

C. 31 131

Step-by-step solution

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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