An engineering professor acquires a new computer once every 2 years. The professor can choose from three models: M1, M2, and M3. If the present model is M1, the next computer can be M2 with probability .2, or M3 with probability .15. If the present model is M2, the probabilities of switching to M1 and M3 are .6 and .25, respectively. And, if the present model is M3, then the probabilities of purchasing M1 and M2 are .5 and .1, respectively.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter9: Decision Making Under Uncertainty
Section: Chapter Questions
Problem 70P
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 Represent the situation as a Markov chain. 

 Determine the probability that the professor will purchase the current model (M1, M2, M3) in 4 years. 

 

An engineering professor acquires a new computer once every 2 years. The professor can choose
from three models: M1, M2, and M3. If the present model is M1, the next computer can be M2 with
probability .2, or M3 with probability .15. If the present model is M2, the probabilities of switching to
M1 and M3 are .6 and .25, respectively. And, if the present model is M3, then the probabilities of
purchasing M1 and M2 are .5 and .1, respectively.
Transcribed Image Text:An engineering professor acquires a new computer once every 2 years. The professor can choose from three models: M1, M2, and M3. If the present model is M1, the next computer can be M2 with probability .2, or M3 with probability .15. If the present model is M2, the probabilities of switching to M1 and M3 are .6 and .25, respectively. And, if the present model is M3, then the probabilities of purchasing M1 and M2 are .5 and .1, respectively.
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