a Write down a system of differential equations for the prob

(a) Write down a system of differential equations for the probabilities P_n(t) and the appropriate initial conditions.

(b) Write down an expression in terms of the probabilities P_n(t) for each of the following:

(i) the average queue length of customers in the shop at time t

(ii) the probability that both sales assistants are idle at time t

(iii) the probability that that company earns at least $400 per hour at time t

Solution