If A and B are two events such that P A ∪ B = P A ∩ B , then the incorrect statement amongst the following statements is :

Question

If A and B are two events such that P A ∪ B = P A ∩ B , then the incorrect statement amongst the following statements is :, P A + P B = 1, P A ∩ B ' = 0, A & B are equally likely, P A ' ∩ B = 0

MARKS App · Accepted Answer

P A ∪ B = P A ∩ B Using the addition theorem of probability, P A ∪ B = P A + P B - P A ∩ B ⇒ P A = P B P A ∩ B ' = 0 P A ' ∩ B = 0 Here, A and B are equally likely. But we can't say that P A = P B = 1 2 Therefore, P A + P B ≠ 1

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