Example 2. In a square (Fig. 1.3) with vertices at points $O(0,0)$, $K(0,1)$, $L(1,1)$, $M(1,0)$, a point $Q(x, y)$ is randomly thrown. Find the probability that the coordinates of this point satisfy the inequality $y>\frac{1}{2} x$.
Solution. Draw the line $y=(1 / 2) x$, it will intersect the segment $M L$ at the point $N(1 ; 1 / 2)$. This line divides the plane into two half-planes: for the coordinates of points in the first one (upper) the inequality $y>x / 2$ will be satisfied, for the second (lower) - the inequality $y<x / 2$. The points for which the inequality $y>x / 2$ holds, are located in the polygon $O K L N$. This polygon consists of the rectangle $C K L N$ and the triangle $O C N$, its area $S_{1}=1 / 2+1 / 4=3 / 4$. The area $S$ of the square $O K L M$ is equal to one: $S=1$. According to formula (1.5.1), taking $S_{1}=S_{g}, S=S_{G}$, we find the desired probability

$$
P(A)=\frac{S_{1}}{S}=\frac{3 / 4}{1}=3 / 4=0.75
$$