U bayes theorem for probability revision to compute the

Question

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               s_i                             s₂

Queen City Avenue, d_i         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.

P(C	s 1)        =	0.8	P(0	I s 1) = 0.2            P(R	s 1) =	0.0
P(C	s 2)        =	0.1	P(0	I s2) = 0.3        P(R	I s2) =	0.6

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?