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BITSAT2024MathematicsProbabilityActual

For two events A and B , if P ( A )= P ( A B )= 1 4 and P ( B A )= 1 2 , then which of the following is not true?

Options

  1. AA and B are independent
  2. BP ( A ^ B )= 3 4
  3. CP ( B ^ A ^ )= 1 2
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

P ( B A )= 1 2 P ( B A ) P ( A ) = 1 2 P ( B A )= 1 8 P ( A B )= 1 4 P ( A B ) P ( B ) = 1 4 P ( B )= 1 2 P ( A B )= 1 8 = P ( A ) P ( B ) Events A and B are independent. Now, P ( A ^ B )= P ( A B ) P ( B ) = P ( A ) P ( B ) P ( B ) = 3 4 and P ( B ^ A ^ )= P ( B ^ A ^ ) P ( A ^ ) = P ( B ^ ) P ( A ^ ) P ( A ^ ) = 1 2

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