The Ritz Hotel has enough space for six taxicabs to load passengers, line up, and wait for guests at its entrance. Cabs arrive at the hotel every 10 minutes and if a taxi drives by the hotel and the line is full it must drive on. Hotel guests require taxis every five minutes on average and then it takes a cab driver an average of 3.5 minutes to load passengers and luggage and leave the hotel (exponentially distributed).
a. What is the average time a cab must wait for a fare?
b. What is the probability that the line will be full when a cab drives by and it must drive on?