If $A$ and $B$ an two events such that $P\,(A \cup B) = \frac{5}{6}$,$P\,(A \cap B) = \frac{1}{3}$ and $P\,(\bar B) = \frac{1}{3},$ then $P\,(A) = $

  • A

    $\frac{1}{4}$

  • B

    $\frac{1}{3}$

  • C

    $\frac{1}{2}$

  • D

    $\frac{2}{3}$

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