There is a carnival game called "Spin the Wheels" where there are two fair wheels. You choose a wheel to spin, and then where the needle lands determines the prize you get. Wheel A has a slice that is 1 4 of the circumference with $10 written on it. Wheel B has a slice that covers 1 2 of the circumference with $2 on it, and a small slice that is 1 50 of the circumference with $100 on it. For both wheels, you win $0 for any spin landing outside these slices.

(a) Find the probability that you spin Wheel B five times and win a total of exactly $8.

(b) Suppose you spin both wheels once. Find the probability that you will make at least $12.

(c) How much money do you expect to get from Wheels A and B on one spin on average? Which is better to spin? (

d) Suppose you doubled Wheel A in size, keeping all slices the same fraction of the circumference. How would the probability of winning $10 change?