10. Customers arrive at a one-window drive according to a Poisson distribution with mean of 10 minutes and service time per customer is exponential with mean of 6 minutes. The space in front of the window can accommodate only three vehicles including the serviced one. Other vehicles have to wait outside this space. Calculate:

(i) Probability that an arriving customer can drive directly to the space in front of the window.

(ii) Probability that an arriving customer will have to wait outside the directed space.

(iii) How long an arriving customer is expected to wait before getting the service?

(CA, May, 1998)