Customers place coffee orders on Plymouth Starbucks at a Poisson rate of one coffee order every 2 minutes. If 1/3 of the customers order black coffee (no cream or sugar) then (a) (5 points) what is the probability that at least one black coffee is ordered during a (b) (5 points) given that 12 black coffees were ordered in an hour, what is the expected (c) (5 points) given that 12 black coffees were ordered in an hour, what is the expected total (d) (10 points) if 27 coffees were ordered in an hour, what is the probability that exactly 17 15-minute period? number of coffees with cream or sugar ordered in that time? number of of them had cream or sugar? coffccs ordcred in that timc?