设二维随机变量 $(X, Y)$ 的概率密度为
$$
f(x, y)=\left\{\begin{array}{l}
1,|y| < x, 0 < x < 1, \\
0, \quad \text { 其他. }
\end{array}\right.
$$
则 $P\left\{Y>0 \left\lvert\, X=\frac{1}{2}\right.\right\}=1$,
A
$\frac{1}{6}$
B
$\frac{1}{4}$
C
$\frac{1}{3}$
D
$\frac{1}{2}$
E
F