A typical slot machine in a Nevada has three wheels, each marked with twenty symbols at equal spacing's around the wheel. The machine is engineered so that on each play the three wheels spin independently, and each wheel is equally likely to show any one of its twenty symbols when it stops spinning. On the central wheel, nine out of the twenty symbols are bells, while there is only one bell on the left wheel and one bell on the right wheel. The machine pays out the jackpot only if the wheels come to rest with each wheel showing a bell.
a) Calculate the probability of hitting the jackpot.
b) Calculate the probability of getting two bells but not the jackpot.
c) Suppose that instead there were three bells on the left, one in the middle, and three on the right. How would this affect the probabilities in a) and b)? Explain why the casino might find the 1 -9 -1 machine more profitable than a 3 -1 -3 machine.