The Ritz Hotel has enough space for six taxicabs to loadpassengers, line up, and wait for guests at its entrance. Cabs arrive at the hotel every 10 minutes and if a taxi dri-ves by the hotel and the line is full it must drive on. Hotel guests require taxis every five minutes on average andthen it takes a cab driver an average of 3.5 minutes to load passengers and luggage and leave the hotel (expo-nentially 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 acab drives by and it must drive on?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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 dri-
ves 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 (expo-
nentially 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?

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