If $P(B) = \frac{3}{4}$, $P(A \cap B \cap \bar C) = \frac{1}{3}{\rm{ }}$ and $P(\bar A \cap B \cap \bar C) = \frac{1}{3},$ then $P(B \cap C)$ is

  • [IIT 2003]
  • A

    $\frac{1}{{12}}$

  • B

    $\frac{1}{6}$

  • C

    $\frac{1}{{15}}$

  • D

    $\frac{1}{9}$

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  • [JEE MAIN 2019]

If $A$ and $B$ are two events of a random experiment, $P\,(A) = 0.25$, $P\,(B) = 0.5$ and $P\,(A \cap B) = 0.15,$ then $P\,(A \cap \bar B) = $