The probability that $\sin^{-1} ( \sin \: x)+ \cos^{-1} ( \cos\: y)$ is an integer $x,y \in \{ 1,2,3,4 \}$ is

Question

$\begin {array} {1 1} (A)\;\large\frac{1}{6} & \quad (B)\;\large\frac{3}{16} \\ (C)\;\large\frac{15}{16} & \quad (D)\;None\: of \: these \end {array}$