If 2 real numbers between 0 and 10 are randomly chosen, what is the

Here let the two numbers be x and y.
As these REAL numbers can be anything, 5.5 and 8 or 9 and 7 or 1.1 and 4.5, and are related to each other, the question is testing area concept and we can draw a square on x-y axis.

The value of x and y can vary from 0 to 10, so we draw a square of 10*10 as shown in the figure attached. This square represents all possible combinations of (x,y).

Now we are looking at maximum distance to be 7 between them.
There will be two such cases
1) When x is 0, y can be anything from 7 to 10, and as x increases, the range of y also decreases. This can be depicted by a line joining (0,7) to (3,10). The area between these two points and (0,10) will give all such combinations of real numbers, where y>x.
2) Similarly, the area between (10,0), (7,0) and (10,3) will give the combinations of two real numbers where x>y.

The total area is 10*10=100
Area where the distance is 7 at the most = Total- Area of triangles =\(100-2*(\frac{1}{2}*3*3)=100-9=91\)

Probability of picking numbers or (x,y) in this area = \(\frac{91}{100}=0.91\)


A