For each assume that you pick real numbers a and b at random

For each assume that you pick real numbers a and b at random between 0 and 10.Find the probability of each of the following

1. The circle (x-a)^2+(y-b)^2 =1 lies entirely within a square with opposite vertices (0,0) and (10,10)

Solution

Sides of square = 10

Now for the circle  (x-a)^2+(y-b)^2 =1 lies entirely within a square we must have radius of circle less than equal to 5. Hence we can choose any numbers between 0 to 5. Therefore we have tottal 6 numbers out of 10.

Therefore, probability = 6/10 = 0.6