A and B are events such that _{$P\left(A\cup B\right)=\frac{3}{4}$} ,_{$\left(A\cap B\right)=\frac{1}{4}$} , _{$P\left(\overline{A}\right)=\frac{2}{3}$} then _{$P\left(\overline{A}\cap B\right)$}  is

_{$P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)$}

_{$\Rightarrow \frac{3}{4}=1-P\left(\overline{A}\right)+P\left(B\right)-\frac{1}{4}$}

_{$\Rightarrow 1=1-\frac{2}{3}+P\left(B\right)\Rightarrow P\left(B\right)=\frac{2}{3}$} ;

Now, _{$P\left(\overline{A}\cap B\right)=P\left(B\right)-P\left(A\cap B\right)=\frac{2}{3}-\frac{1}{4}=\frac{5}{12}$}