If A ,   B are two events with P ( A ∩ B ) = 1 3 , P ( A ∪ B ) = 5 6 and P A C = 1 2 , then…

If A, B are two events with P(A∩B)=13,P(A∪B)=56 and PAC=12, then the value of PBC is
  1. 12
  2. 13
  3. 23
  4. 56

Solution

We know that, P(A∪B)=P(A)+P(B)-P(A∩B) and P(A)+P(Ac)=1

Then, P(A∪B)=1-P(Ac)+1-P(Bc)-P(A∩B)

⇒56=1-12+1-P(Bc)-13

⇒PBc=13

Asked in: AP EAMCET 2021 (19 Aug Shift 2)

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