A is targetting to B, b and C are targetting to A. probability of hitting the target by A,B and C are $\large\frac{2}{3}, \large\frac{1}{2} \: and \: \large\frac{1}{3}$ respectively. If A is hit then the probability that B hits the target and C does not is

Question

$\begin {array} {1 1} (A)\;\large\frac{1}{2} & \quad (B)\;\large\frac{3}{4} \\ (C)\;\large\frac{2}{3} & \quad (D)\;None\:of \: these \end {array}$