Sumayya is considering purchasing a vehicle for her daily commute from her off-campus housing. After researching her options, she has narrowed them down to a used sedan she found in SUPost, a certified pre-owned car from Towne Mazda, and a new Vespa from CalMoto. She thinks there is a possibility that she will have next summer off, and ideally the vehicle she purchases would be useful for doing a road trip. She believes that there is a 0.6 probability of having next summer off. Additionally, she is worried that due to the lack of knowledge of the used sedan's condition it might break down during a long trip. She assigns a 0.3 probability of the sedan breaking down during a long trip.

The following decision tree captures her beliefs about the decision problem and the value she assigns to each outcome (after accounting for the cost of acquiring the vehicles): Dollar value 0.3 Breaks down $200.00 0.6 Summer off 0.7 No breakdown Used sedan $1,500.00 0.4 Busy summer $600.00 0.6 Summer off $1,400.00 Certified pre-owned 0.4 Busy summer $450.00 0.6 Summer off $900.00 New Vespa 0.4 Busy summer $750.00 You know that Sumayya is risk neutral for the range of prospects in the deal. Consider the following statements: I. Sumayya should purchase the used sedan. II. Sumayya should be willing to pay a positive amount for clairvoyance on whether the used sedan will break down during a long trip. III. Sumayya should be willing to pay at least $100 for clairvoyance on whether she will have next summer off. How many of the statements must be true? a) W N