$P(A \cup B) = P(A \cap B)$ if and only if the relation between $P(A)$ and $P(B)$ is

  • [IIT 1985]
  • A

    $P(A) = P(\bar A)$

  • B

    $P\,(A \cap B) = P(A' \cap B')$

  • C

    $P\,(A) = P\,(B)$

  • D

    None of these

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  • [IIT 1989]

$A$ and $B$ are two events such that $P(A)=0.54$, $P(B)=0.69$ and $P(A \cap B)=0.35.$ Find $P \left( B \cap A ^{\prime}\right)$.

Fill in the blanks in following table :

$P(A)$ $P(B)$ $P(A \cap B)$ $P (A \cup B)$
$0.35$  ........... $0.25$  $0.6$