It is given that the events A and B are such that $P(A) = \large\frac{1}{4}\: \: P \bigg( \large\frac{A}{B} \bigg) \large\frac{1}{2}\: and \: P \bigg( \large\frac{B}{A} \bigg) = \large\frac{2}{3}$ Then $P(B)$ is

Question

$\begin {array} {1 1} (A)\;\large\frac{1}{6} & \quad (B)\;\large\frac{1}{3} \\ (C)\;\large\frac{2}{3} & \quad (D)\;\large\frac{1}{2} \end {array}$