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COMEDK2024MathematicsProbability

If A and B are events, such that P(A)= 1 4 P ( A B )= 1 2 and P ( B A )= 2 3 then P(B) is

Options

  1. A1 3
  2. B2 3
  3. C1 2
  4. D1 6

Correct answer

B. 2 3

Step-by-step solution

Given, P(A)= 1 4 , P ( A B )= 1 2 and P ( B A )= 2 3 We know that, P ( E₁ E₂ )= P (E₁ E₂ ) P (E₂ ) P ( B A )= P(A B) P(A) aligned 2 3 1 4 & =P(A B) 1 6 =P(A B) P ( A B ) & = P(A B) P(B) P(B) & = 1 6 4 1 P(B) & = 2 3 aligned

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