In one of the games at the county fair, people pay to shoot a paint pistol at the target shown below right. The center has a radius of one inch. Each concentric circle has a radius one inch larger than the preceding circle. Assuming the paint pellet hits the target randomly, what is the probability that it hits:

1. The $50$-point ring?

   Hint (a):

   Area of a circle = πr²

   More Help (a):

   $P(50pt)=\frac{\text{area of success}}{\text{total area}}=\frac{\pi(1)^{2}}{\pi(4)^{2}}$

   Answer (a)

   $\frac{1}{16}$

2. The $20$-point ring?

   Hint (b):

   $P(20pt)=\frac{\text{area of success}}{\text{total area}}=\frac{\pi(2)^{2}-\pi(1)^{2}}{\pi(4)^{2}}$