# Finding probability of two numbers which satisfies an inequality

1. Nov 10, 2012

### justwild

1. The problem statement, all variables and given/known data

Two numbers x and y are selected from a closed interval [0,4]. To find the probability that the two numbers satisfies the condition that y$^{2}$$\leq$ x.

2. The attempt at a solution

Don't have any idea

2. Nov 10, 2012

### HallsofIvy

Staff Emeritus
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.

3. Nov 10, 2012

### justwild

Gotcha..thanks for the help