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KCET2023MathematicsProbability

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

A. 1 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 ) aligned & 2 3 = P(A B) 1 / 4 [ A B=B A] & P(A B)= 2 3 1 4 = 1 6 aligned P ( A B )= 1 2 P(A B) P(B) = 1 2 P(B)=2 P(A B)=2 1 6 = 1 3

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