It is given that the events $A$ and $B$ are such that $P\left( A \right) = {1 \over 4},P\left( {A|B} \right) = {1 \over 2}$ and $P\left( {B|A} \right) = {2 \over 3}.$ Then $P(B)$ is :

Question

It is given that the events $A$ and $B$ are such that
$P\left( A \right) = {1 \over 4},P\left( {A|B} \right) = {1 \over 2}$ and $P\left( {B|A} \right) = {2 \over 3}.$ Then $P(B)$ is :

${1 \over 6}$