To save on expenses, Rona and Jerry agreed to form a carpool for traveling to and from work. Rona preferred to use the somewhat longer but more consistent Queen City Avenue. Although Jerry preferred the quicker expressway, he agreed with Rona that they should take Queen City Avenue if the expressway had a traffic jam. The following payoff table provides the one-way time estimate in minutes for traveling to and from work. DecisionAlternative State of Nature ExpresswayOpen s1 ExpresswayJammed s2 Queen City Avenue, d1 35 35 Expressway, d2 30 50 Based on their experience with traffic problems, Rona and Jerry agreed on a 0.05 probability that the expressway would be jammed. In addition, they agreed that weather seemed to affect the traffic conditions on the expressway. Let C = clear O = overcast R = rain The following conditional probabilities apply. P(C|s1) = 0.8 P(C|s2) = 0.1 P(O|s1) = 0.2 P(O|s2) = 0.3 P(R|s1) = 0.0 P(R|s2) = 0.6. Use Bayes' theorem for probability revision to compute the probability of each weather condition and the conditional probability of the expressway open,  s1,  or jammed,  s2,  given each weather condition. (Round the probability of each weather condition to three decimal places and the conditional probabilities to two decimal places.).  Show the decision tree for this problem.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section5.3: Assignment Models
Problem 10P
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To save on expenses, Rona and Jerry agreed to form a carpool for traveling to and from work. Rona preferred to use the somewhat longer but more consistent Queen City Avenue. Although Jerry preferred the quicker expressway, he agreed with Rona that they should take Queen City Avenue if the expressway had a traffic jam. The following payoff table provides the one-way time estimate in minutes for traveling to and from work.
Decision
Alternative
State of Nature
Expressway
Open s1
Expressway
Jammed s2
Queen City Avenue, d1 35 35
Expressway, d2 30 50
Based on their experience with traffic problems, Rona and Jerry agreed on a 0.05 probability that the expressway would be jammed.
In addition, they agreed that weather seemed to affect the traffic conditions on the expressway. Let
C = clear
O = overcast
R = rain
The following conditional probabilities apply.
  • P(C|s1) = 0.8
  • P(C|s2) = 0.1
  • P(O|s1) = 0.2
  • P(O|s2) = 0.3
  • P(R|s1) = 0.0
  • P(R|s2) = 0.6. Use Bayes' theorem for probability revision to compute the probability of each weather condition and the conditional probability of the expressway open, 
    s1,
     or jammed, 
    s2,
     given each weather condition. (Round the probability of each weather condition to three decimal places and the conditional probabilities to two decimal places.).  Show the decision tree for this problem.
  •  
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