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MHT CET202615 April 2026Morning ShiftMathematicsProbabilityActual

If A and B are two events such that P(A) = 2 3 , P(B) = 1 2 and P(A B) = 2 3 , then P(A' B) + P(A B') =

Options

  1. A2 3
  2. B1
  3. C3 2
  4. D5 6

Correct answer

C. 3 2

Step-by-step solution

Given P(A) = 2 3 , P(B) = 1 2 , P(A B) = 2 3 P(A B) = P(A B) P(B) = 2 3 1 2 = 1 3 P(A' B) = 1 - P(A B') = 1 - (P(A) - P(A B)) P(A' B) = 1 - ( 2 3 - 1 3 ) = 2 3 P(A B') = 1 - P(A' B) = 1 - (P(B) - P(A B)) P(A B') = 1 - ( 1 2 - 1 3 ) = 5 6 P(A' B) + P(A B') = 2 3 + 5 6 = 9 6 = 3 2

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