Mathematics - Probability Question with Solution | TestHub

$P(A\cup B)=P(A)+P(B)-P(A\cap B)\Rightarrow \frac{3}{4}=1-P(\bar{A})+P(B)-\frac{1}{4}$ $\Rightarrow 1=1-\frac{2}{3}+P(B)\Rightarrow P(B)=\frac{2}{3};$ Now, $P(\bar{A}\cap B)=P(B)-P(A\cap B)=\frac{2}{3}-\frac{1}{4}=\frac{5}{12}$