设 $(X, Y)$ 服从二维正态分布 $N\left(0,0, \frac{1}{2}, \frac{1}{2} ; 0\right), \Phi(x)$ 为标准正态分布函数，则 $P\{X-Y < E(|X-Y|)\}=(\quad)$
A. $\Phi\left(\frac{1}{2}\right)$
B. $\Phi(\sqrt{2})$
C. $\Phi\left(\sqrt{\frac{2}{\pi}}\right)$
D. $\Phi\left(\frac{\sqrt{2}}{\pi}\right)$