Question

Can anyone please help me with this question? : A target consists of two concentric circles. The larger circle has diameter 1m. When a complete novice fires at the target, the probability of hitting the blue circle is the same as the probability of hitting the green region. Find the diameter of the blue circle.

Answer 1

We know that
if  the probability of hitting the blue circle is the same as the probability of hitting the green region
then 
the area of the blue circle is equal to the area of the green region

Let
x----> diameter of the blue circle

area of the blue circle=pi*(x/2)²----> (pi/4)*x² m²-----> equation 1

area of the green region=area of the larger circle-area of the blue circle
area of the green region=pi*(1/2)²-(pi/4)*x²
=(pi/4)-(pi/4)*x² m²----> equation 2

equate equation 1 and equation 2
(pi/4)*x²=(pi/4)-(pi/4)*x² -----> divide by (pi/4)---> x²=1-x²
2x²=1-----> x²=1/2----> x=1/√2-----> x=√2/2 m

the diameter of the blue circle is √2/2 m