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)= (\pi r^2)/(\pi R^2) = (\pi 2^2)/(\pi 6^2) = (4)/(36) = (1)/(9)`.
The probability that arrow hits the red region Y is:


`P(Y)= (\pi R^2-\pi r^2)/(\pi R^2) = (\pi 6^2-\pi 2^2)/(\pi 6^2) = (32)/(36) = (8)/(9)`.