The Ritz Hotel has enough space for 6 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 5 minutes on average. 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? (Ans is 17.34 mins)

Looking for the steps in between. Thank you.

b. What is the probability that the line will be full when a cab drives by and it must drive on? (Ans is 0.0006)