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

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It is given that $P ( A )=0.54$,  $P ( B )=0.69$,  $P (A \cap B)=0.35$

$A^{\prime} \cap B^{\prime}=(A \cup B)^{\prime}$         [by De Morgan's law]

$\therefore P \left(A^{\prime} \cap B^{\prime}\right)$ $= P (A \cup B)^{\prime}=1- P (A \cup B)=1-0.88=0.12$

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