Free SAT Practice Question

A circular emblem of radius \(4\) centimeters is printed on a badge. Two concentric circles are drawn on it, one of radius \(2\) centimeters and one of radius \(3\) centimeters, dividing the emblem into three regions: a center disk (out to radius \(2\)), a middle ring (from radius \(2\) to radius \(3\)), and an outer ring (from radius \(3\) to radius \(4\)). The center disk and the outer ring are colored gold; the middle ring is left plain. If a point on the emblem is chosen at random, what is the probability that it lies in a gold region?