There is a green square board of side ' $2 a$ ' unit circumscribing a red circle. Jayadev is asked t

Question

There is a green square board of side ' $2 a$ ' unit circumscribing a red circle. Jayadev is asked to keep a dot on the above said board. Find the probability that he keeps the dot on the green region.\

Professor PC Thomas Classes · Answer

(b) : Area of square $=(2 a)^{2}=4 a^{2}$ 
Area of circle $=\pi a^{2}$\ $P$ (Dot on the green region)\ $=\frac{	ext { Area of square }- 	ext { Area of circle }}{	ext { Total Area }}$\ $=\frac{4 a^{2}-\pi a^{2}}{4 a^{2}}=\frac{a^{2}(4-\pi)}{4 a^{2}}=\frac{4-\pi}{4}$