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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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Transcribed Image Text:3. Suppose that a car rental agency has three locations, numbered 1, 2, and 3. A customer may rent a car
from any of the three locations and return it to any of the three locations. Records show that cars are
rented and returned in accordance with the following probabilities:
Rented from Location
2
3
1
0.3
0.4
0.1
Rented
2
0.2
0.2
0.3
to
Location
3
0.5
0.4
0.6
a. Assuming that a car is rented from location 1, Calculate the probability that it will be at
location 1 after two rentals?
b. Assuming that this dynamical system can be modeled as a Markov chain, Compute the
steady-state vector.
c. If the rental agency owns 120 cars, how many parking spaces should it allocate at each
location to be reasonably certain that it will have enough spaces for the cars over the
long term? Explain your reasoning.
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