a carnival has a dart game consisting of three circles with different payoffs as: C $$1,$ B $$5,$ A $$20.$ Over time the operator has learned that when a customer throws a dart, they hit each region with the fol$-$

lowing probabilities: p$($A$)=0\mathrm{.}02,$ p$($B$)=0\mathrm{.}06,$ and p$($C$)=0\mathrm{.}1.$

a$)$ What is the expected payoff for one throw of a dart?

b$)$ If a customer pays $$5$ to throw $3$ darts, how much can the carnival expect to make per customer? $($If a

customer throws all three darts in A they win $$20+$ $$20+$ $$20=$ $$60,$ etc....$)$