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The probability of an event A is 4 5 . The probability of an event B , given that the event A occurs is 1 5 . The probability of event A , given that the event B occurs is 2 3 . The probability that neither of the events occurs is

Options

  1. A3 25
  2. B2 5
  3. C1 25
  4. D2 15

Correct answer

A. 3 25

Step-by-step solution

P A = 4 5 ,   P B A = P A ∩ B P A = 1 5 ⇒ P A ∩ B = 4 25 P A B = P A ∩ B P B = 2 3 ⇒ P B = 4 25 × 3 2 = 6 25 P A c ∩ B c = P A ∪ B c = 1 - P A ∪ B = 1 - P A - P B + P A ∩ B = 1 - 4 5 - 6 25 + 4 25 = 3 25

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