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AP EAMCET202119 Aug 2021Evening ShiftMathematicsProbabilityActual

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

Options

  1. A1 2
  2. B1 3
  3. C2 3
  4. D5 6

Correct answer

B. 1 3

Step-by-step solution

We know that, P ( A ∪ B ) = P ( A ) + P ( B ) - P ( A ∩ B ) and P ( A ) + P ( A c ) = 1 Then, P ( A ∪ B ) = 1 - P ( A c ) + 1 - P ( B c ) - P ( A ∩ B ) ⇒ 5 6 = 1 - 1 2 + 1 - P ( B c ) - 1 3 ⇒ P B c = 1 3

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