Reference no: EM131037044
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 or from work.
State of Nature
Expressway Expressway
Open Jammed
Decision Alternative si s2
Queen City Avenue, di 30 30
Expressway, d2 25 45
Based on their experience with traffic problems, Rona and Jerry agreed on a 0.15 proba¬bility that the expressway would be jammed.
In addition, they agreed that weather seemed to affect the traffic conditions on the ex¬pressway. Let
C = clear
0 = overcast
R = rain
The following conditional probabilities apply.
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P(C
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s 1) =
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0.8
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P(0
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I s 1) = 0.2 P(R
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s 1) =
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0.0
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P(C
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s 2) =
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0.1
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P(0
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I s2) = 0.3 P(R
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I s2) =
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0.6
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a. 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.
b. Show the decision tree for this problem.
c. What is the optimal decision strategy, and what is the expected travel time?
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: 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. Show the decision tree for this problem.
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