Customers arrive at a caf according to a Poisson process at the rate of one every three minutes. Each customer can choose to either sit in the caf or have a takeaway. The takeaway option is chosen by 39% of customers. Whether a customer chooses to sit in or have a takeaway is assumed to be independent of the choices made by other customers. (a) Calculate the probability that exactly three customers arrive in a 15 minute period. (b) Calculate the probability that, in a 15 minute period, at least two customers who have their order as a takeaway arrive at the caf. (c) Calculate the probability that, in a 15 minute period, no sit in customers arrive but at least two takeaway customers arrive at the caf.