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JEE Main20258 Apr 2025Evening ShiftMathematicsProbabilityActual

If A and B are two events such that P(A)=0.7 , P ( B )=0.4 and P ( A B )=0.5 , where B denotes the complement of B , then P(B (A B )) is equal:-

Options

  1. A1 4
  2. B1 2
  3. C1 6
  4. D1 3

Correct answer

A. 1 4

Step-by-step solution

aligned & P ( A )= 7 10 , P ( B )= 4 10 & P ( A B )= 5 10 & P ( B A B )= P ( B ( A B )) P ( A B ) & = P (( B B ) ( B A )) P ( A B ) = P ( A B ) P ( A B ) aligned aligned & = P ( A )- P ( A B ) P ( A )+ P ( B )- P ( A B ) = 7 10 - 5 10 7 10 + (1- 4 10 )- 5 10 & = 2 8 = 1 4 aligned

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