设 $(X, Y)$ 服从二维正态分布, 其概率密度为
$$
f(x, y)=\frac{1}{2 \pi \times 10} \cdot \mathrm{e}^{-\frac{1}{2}\left(\frac{x^2}{10}+\frac{y^2}{10}\right)},-\infty < x < +\infty,-\infty < y < +\infty,
$$
则概率 $P\{X < Y\}=$
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$