Draw a graph. First draw the parabola representing the function x= y^2, then draw the four line segments x= 0, y= 0, x= 4, y= 4 making a square, with vertices (0, 0), (16, 0), (16, 16), and (0, 16), and having the graph x= y^2, which is the same as y= x^{1/2}, crossing the square from (0, 0) to (4, 2). The set of points such that y^2\le x with x and y from [0, 4] is the set of point below that graph. Assuming all values of x and y between 0 and 4 are "equally likely, then all points in the square are "equally likely" and the probability a point is below the parabola is the ratio of the area under the parabola to the area of the square. Find that area by integrating x^{1/2} from x= 0 to x= 4 and then divide by the area of the square, 16.
