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Probability
Question
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Two events A and B will be independent, if

  • A and B are mutually exclusive
  • P(A'B') = [1 - P(A)] [1 - P(B)]
  • P(A) = P(B)
  • P(A) + P(B) = 1

Answer

B.

P(A'B') = [1 - P(A)] [1 - P(B)]

 P(A'B') = (P(A' ∩ B') = P(A ∪ B)'
= 1 - P(A ∪ B)
= 1 - [P(A) + P(B) - P(A ∩ B)]
= 1 - P(A) - P(B) + P(A ∩ B)
= 1 - P(A) - P(B) + P(A) P(B)    [A and B are independent]
= [1 - P(A)] [1 - P(B)]
∴ (B) is correct answer.

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