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If A and B are two events such that P A = 1 3 , P B = 1 5 and P A ∪ B = 1 2 , then P A B ' + P B A ' is equal to

Options

  1. A3 4
  2. B5 8
  3. C5 4
  4. D7 8

Correct answer

B. 5 8

Step-by-step solution

Given, P A = 1 3 , P B = 1 5 and P A ∪ B = 1 2 We know that, P A ∪ B = P A + P B - P A ∩ B ⇒ P A ∩ B = 1 3 + 1 5 - 1 2 = 1 30 Now P A ∩ B ' = Only A = 1 3 - 1 30 = 9 30 And P B ∩ A ' = Only B = 1 5 - 1 30 = 5 30 Now, P A ∣ B ' + P B ∣ A ' = P A ∩ B ' P B ' + P B ∩ A ' P A ' = 9 30 4 5 + 5 30 2 3 = 5 8

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