In a game of darts, the board looks like in the following plot, where the numbers on the plot indicate the radius of each of the circles (the inner most circle has radius 0.2, the second smallest circle has radius 0.4, etc).

Assume that when playing, you never miss the board, and you hit each ring with probability proportional to its area. The points gained by hitting each area are 20 for the inner most, followed by 10, 5, 2, and 1 for the outer most.

(a) Calculate the expected value and variance of X, the number of points from a single throw.

(b) Assume now that, when throwing a dart, you miss the board (accumulating 0 points) 20% of the

time. What is your answer for part (a)?