What is the probability that a number selected from the number 1,2,3...., 25 is a prime number, when each of the given numbers is equally likely to be selected?

Explanation

Area of the shaded region = Area of the square -4 times Area of the sector of the circle

area of a circle `=(2 times 2)-4 times frac{1}{4}(pi)(1)^{2}=4-pi`

Required probability`= frac{ Area of shaded region }{ Area of square }=frac{4-pi}{4}`