$A$ and $B$ are two events such that $P(A)=0.54$, $P(B)=0.69$ and $P(A \cap B)=0.35.$ Find $P \left( B \cap A ^{\prime}\right)$.
$A$ and $B$ are two events such that $P(A)=0.54$, $P(B)=0.69$ and $P(A \cap B)=0.35.$ Find $P \left( B \cap A ^{\prime}\right)$.
It is given that $P ( A )=0.54$, $P ( B )=0.69$, $P (A \cap B)=0.35$
We know that
$n\left( B \cap A ^{\prime}\right)=n( B )-n( A \cap B )$
$\Rightarrow \frac{n\left( B \cap A ^{\prime}\right)}{n( S )}$ $=\frac{n( B )}{n( S )}-\frac{n( A \cap B )}{n( S )}$
$\therefore P \left( B \cap A ^{\prime}\right)= P ( B )- P ( A \cap B )$
$\therefore P \left( B \cap A ^{\prime}\right)=0.69-0.35=0.34$
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- [IIT 1990]
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