question_answer

If \[P(A)=\frac{1}{4,}\] \[P(B)=\frac{1}{5}\] and \[P(A\,\cap B)=\frac{1}{7},\]find \[P(\bar{A}\,/\bar{B}).\]

Answer:

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