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

Options

  1. AP A + P B = 1
  2. BP A ∩ B ' = 0
  3. CA   &   B are equally likely
  4. DP A ' ∩ B = 0

Correct answer

A. P A + P B = 1

Step-by-step solution

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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