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JEE Math Practice Question

It is given that the events $$A$$ and $$B$$ are such that $$P\left( A \right) = {1 \over 4},P\left( {A|B} \right) = {1 \over 2}$$ and $$P\left( {B|A} \right) = {2 \over 3}.$$ Then $$P(B)$$ is :

  1. A.$${1 \over 6}$$
  2. B.$${1 \over 3}$$
  3. C.$${2 \over 3}$$
  4. D.$${1 \over 2}$$

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