A and B are two events such that $P(A ∪ B)=\frac{3}{4}, P(A ∩ B)=\frac{1}{4}, P(\overline{A})=\frac{2}{3}$, then $P(\overline{A} ∩ B)= $

$\frac{5}{12}$

Since A and $\overline{A} ∩ B $ are mutually exclusive events such that

$A ∪ B= A ∪ (\overline{A} ∩ B)$

$⇒P(A  ∪  B)=P(A) +P(\overline{A} ∩ B) $

$⇒ \frac{3}{4}=\frac{1}{3}+P(\overline{A} ∩ B)⇒P(\overline{A} ∩ B)=\frac{5}{12}$