Two points are selected randomly on a line of length 32 so as to be on opposite sides of the midpoint of the line. In other words, the two points X and Y are independent random variables such that X is uniformly distributed over [0,16) and Y is uniformly distributed over (16,32]. Find the probability that the distance between the two points is greater than 9.

Solution :

Let us consider the squares be

If x ranges from the 0 to 16 and the y ranges from 16 to 32, we see that the boundary of the region  which goes from the .

And so it is easier to find the area of region where . This is the triangle with points as its vertices.

The area if the triangle is =  

                                         =

Now the entire area is  = 256

Then,

or

Thus the answer is

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step-by-step explanation: