31. The postoffice of a certain small town has only one clerk to wait on customers. The probability that a customer will be served in any given minute is 0.6, regardless of the time that the customer has already taken. The probability of a new customer arriving is 0.45, regardless of the number of customers already in line. The chances of two customers arriving during the same minute are negligible. Similarly, the chances of two customers being served in the same minute are negligible. Suppose that we start with exactly two customers: one at the postal window and one waiting on line. After 4 minutes, what is the probability that there will be exactly four customers: one at the window and three waiting on line?
I know that this will use the formula for binomial random variables, bt I'm not sure where to begin with this one, as there's two different probabilities to take into account.