• # question_answer If $P(A)=\frac{1}{4,}$ $P(B)=\frac{1}{5}$ and $P(A\,\cap B)=\frac{1}{7},$find $P(\bar{A}\,/\bar{B}).$

Given, $P(A)=\frac{1}{4},$ $P(B)=\frac{1}{5}$ and $P(A\,\cap B)=\frac{1}{7}$ $\therefore$ $P\left( \frac{{\bar{A}}}{B} \right)=\frac{P(\bar{A}\cap \bar{B})}{P(\bar{B})}=\frac{1-P(A\cup B)}{1-P(B)}$ $=\frac{1-[P(A)+P(B)-P(A\cap B)]}{1-\frac{1}{5}}$        $=\frac{97}{28\times 4}=\frac{97}{112}$