If A and B are two events such that P A ∪ B = P A ∩ B , then the incorrect statement amongst the…

If Aand B are two events such that PA∪B=PA∩B, then the incorrect statement amongst the following statements is :
  1. PA+PB=1
  2. PA∩B'=0
  3. A & B are equally likely
  4. PA'∩B=0

Solution

PA∪B=PA∩B

Using the addition theorem of probability, 

PA∪B=PA+PB-PA∩B

⇒PA=PB

PA∩B'=0

PA'∩B=0

Here, A and B are equally likely.

But we can't say that PA=PB=12

Therefore, PA+PB≠1

Asked in: JEE Main 2014 (09 Apr Online)

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