jmc

The total area of the target is $\pi \cdot 10^2=100\pi$. The area of the inner shaded region is the area of a circle with radius 4, and that is equal to $\pi \cdot 4^2=16\pi$. We can calculate the area of the shaded ring as the difference in areas of a circle with radius 8 and with radius 6. This gives an area of $\pi \cdot 8^2-\pi \cdot 6^2=28\pi$. The total shaded area is $16\pi +28\pi =44\pi$. The probability a dart will hit a shaded region is equal to $\frac{44\pi }{100\pi }=\boxed{\frac{11}{25}}$.