Question

. An archery target is shown. The radius of region X is 2 ft and the radius of the entire target is 6 ft. If an arrow hits the target at random, what is the probability that it hits the red region Y? Round to the nearest percent.

Answer 1

The target with regions X and Y is shown on the added image.
The probability that arrow hits the red region X is:

$P(X)= \dfrac{\pi r^2}{\pi R^2} = \dfrac{\pi 2^2}{\pi 6^2} = \dfrac{4}{36} = \dfrac{1}{9}$.
The probability that arrow hits the red region Y is:

$P(Y)= \dfrac{\pi R^2-\pi r^2}{\pi R^2} = \dfrac{\pi 6^2-\pi 2^2}{\pi 6^2} = \dfrac{32}{36} = \dfrac{8}{9}$.