jmc

First, the total area of the radius $3$ circle is simply just $9\ast \pi$ when using our area of a circle formula. Now from here, we have to find our shaded area. This can be done by adding the areas of the $3$ $\frac{1}{2}$-radius circles and add; then, take the area of the $2$ radius circle and subtract that from the area of the $2$ radius 1 circles to get our resulting complex area shape. Adding these up, we will get $3\ast \frac{1}{4}\pi +4\pi -\pi -\pi =\frac{3}{4}\pi +2\pi =\frac{11\ast \pi }{4}$. So, our answer is $\frac{\frac{11}{4}\pi }{9\pi }=\boxed{\frac{11}{36}}$.