$.(30$pts$)$ A ISEN student gets a job managing a movie theater. After a couple of days on the job, he notices that prior to $6$:$00$pm people arrive to buy tickets according to a Poisson process with an average rate of $10$ customers per hour. Only one cashier is at the window during these non$-$peak hours. The time it takes the cashier to complete a ticket sales transaction is exponentially distributed with $=30/$hour$.$ If a customer arrives and finds the cashier busy, they join a queue that operates in a first$-$come, firstserved manner. $($a$)$ What is the probability that an arriving customer has to wait in line? $($b$)$ How many customers on average are either at the window or in line? $($c$)$ What is the average waiting time of a customer?