在区间$[0,1]$上随机取两个数$x,y$，记$p_1$为事件"$x+y\ge \frac{1}{2}$"的概率，$p_2$为事件"$\left|x+y\right|\le \frac{1}{2}$"的概率，$p_3$为事件"$xy\le \frac{1}{2}$"的概率，则

$p_1<p_2<p_3$ $p_2<p_3<p_1$ $p_3<p_1<p_2$ $p_3<p_2<p_1$