1. Determine the optimal decision for Bob and Harry if they wish to minimise the travel time.

2. What is the expected value of perfect information?

3.

Additionally, Bob and Harry can get road condition updates from traffic broadcasts. The broadcast can return positive, neutral, negative results? Let P = positive; N = neutral; G = negative. The following conditional probabilities apply.

Apply the Bayes Theorem to compute joint probabilities and posterior probabilities.

Please use the below information to answer Questions 1.1 to 1.5. To save on expenses, Bob and Harry agreed to form a carpool for traveling to and from work in Caulfield. Bob preferred to use the somewhat longer but more consistent National Route Alt 1. Although Harry preferred the quicker Motorway 1, he agreed with Bob that they should take National Route Alt 1 if the Motorway 1 had a traffic jam. Based on their experience with traffic problems, Bob and Harry agreed on a 0.15 probability that the Motorway 1 could be jammed, otherwise, it will be open. The following payoff table provides the one-way time estimate in minutes for traveling to or from work. Decision Alternative M1 open (S1) M1 jammed (S2) Alt 1 30 30 M1 25 45 = = = P (P \si) = 0.8, P (N (S1) = 0.2, P (G |81) = 0.0 P (P 182) = 0.1, P (N 182) = 0.3, P (G \s2) = 0.6 = = = Please use the below information to answer Questions 1.1 to 1.5. To save on expenses, Bob and Harry agreed to form a carpool for traveling to and from work in Caulfield. Bob preferred to use the somewhat longer but more consistent National Route Alt 1. Although Harry preferred the quicker Motorway 1, he agreed with Bob that they should take National Route Alt 1 if the Motorway 1 had a traffic jam. Based on their experience with traffic problems, Bob and Harry agreed on a 0.15 probability that the Motorway 1 could be jammed, otherwise, it will be open. The following payoff table provides the one-way time estimate in minutes for traveling to or from work. Decision Alternative M1 open (S1) M1 jammed (S2) Alt 1 30 30 M1 25 45 = = = P (P \si) = 0.8, P (N (S1) = 0.2, P (G |81) = 0.0 P (P 182) = 0.1, P (N 182) = 0.3, P (G \s2) = 0.6 = = =