# To save on expenses, Rona and Jerry agreed to form a carpool for traveling to and...

###### Question:

To save on expenses, Rona and Jerry agreed to form a carpool for traveling to and from work. Rona prefers to use the somewhat longer but more consistent Queen City Avenue. Although Jerry prefers the quicker expressway, he agreed with Rona that they should take Queen City Avenue if the expressway has 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 Open Expressway Jammed Decision Alternative S1 S2 Queen City Avenue, di 30 30 Expressway, d2 25 45 Based on their experience with traffic problems, Rona and Jerry agreed on a 0.25 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 0 = overcast R = rain The following conditional probabilities apply: P( CS1) = 0.8 PCOS1) = 0.2 PCR | S1) = 0.0 P(C | $2) = 0.1 P(O 52) = 0.3 P(R |$2) = 0.6 (a) Use Bayes' theorem for probability revision to compute the probability of each weather condition and the conditional probability of the expressway being open, s 1, or jammed, s 2, given each weather condition. If required, round your answers to three decimal places. If your answer is zero enter "O". P(si C): 0.987 P(S2C): 0.022 P(sı O): 0.791 P(S2O): 0.209
(c) What is the optimal decision strategy? Choose the correct answer below. (i) Do not check the weather, and take the Expressway. (ii) Do not check the weather, and take Queen City Ave. (iii) Check the weather, and only take the Expressway if it rains. (iv) Check the weather, and only take the Queen City Ave. if it rains. (v) Check the weather, and only take the Expressway if weather is clear. Option (v) What is the minimum expected travel time? If required, round your answer to one decimal place. Do not round intermediate calculation. 26.6 minutes

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