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If A and B are any two events such that P A = 2 5 and P A ∩ B = 3 20 , then the conditional probability, P A A ′ ∪ B ′ , where A ' denotes the complement of A , is equal to :

Options

  1. A11 20
  2. B5 17
  3. C8 17
  4. D1 4

Correct answer

B. 5 17

Step-by-step solution

Given P A = 2 5 = 8 20 &   P A ∩ B = 3 20 ∴     P A ' ∪ B ' = P A ∩ B ' = 1 - P A ∩ B = 1 - 3 20 = 17 20 P A ∩ A ' ∪ B ' = P A ∩ B ' = P A - P A ∩ B = 8 20 - 3 20 = 5 20     ∴     P A A ' ∪ B ' = P A ∩ A ' ∪ B ' P A ' ∪ B ' = 5 20 17 20 = 5 17

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