2. You are preparing to go for a bike ride and are trying to decide whether to use your thin road tires or your thicker, knobbier tires. The advantage of the thin road tires is that you can ride much faster. But, you know from previous experience that your road tires are more likely to go flat during a ride. There is a 40% chance your road tires will go flat but only a 10% chance that the thicker tires will go flat. Because of the risk of a flat, you also have to decide whether or not to bring your tools along on the ride (a pump, tire levers and a puncture kit). These tools will weigh you down.
The utilities of different cases are given in Table Q2 below.
Which tire to use Whether tire goes flat Whether to bring tools Utility
Road tire Yes Yes 50
Thicker tire Yes Yes 40
Road tire No Yes 75
Thicker tire No Yes 65
Road tire Yes No 0
Thicker tire Yes No 0
Road tire No No 100
Thicker tire No No 75
(a) What are the three types of nodes in a decision network for this problem? Draw the decision network. (10 marks)
(b) What is the optimal decision? What is the expected utility of the optimal decision? Show clearly the detailed steps of deriving your answers. (15 marks)
