If $A$ and $B$ are two events with $P(A \cap B) = \frac{1}{3}$,$P(A \cup B) = \frac{5}{6}$,and $P(A^C) = \frac{1}{2}$,then the value of $P(B^C)$ is

  • A
    $\frac{1}{2}$
  • B
    $\frac{1}{3}$
  • C
    $\frac{2}{3}$
  • D
    $\frac{5}{6}$

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