what is the probability that $y\le \sin x$? We need to find in a rectangle $[0,{\pi\over 2}]\times [0,1]$ a point $(x,y)$ is chosen at random what is the probability that $y\le \sin x$?
Will it be $${\int_{0}^{\pi/2} \sin x \ dx\over \pi/2}$$

The distribution of the point $(x,y)$ is uniform on the rectangle.  Therefore, you just divide the area of the region where $y \le \sin(x)$ by the area of the entire region.  
