R Figure 2: The Bayesian network required for Q3 (b). (b) Uncertainty. Consider the following simple description of faults in the brakes of a bus. Two problems may cause a brake repair to be...

Extracted text: R Figure 2: The Bayesian network required for Q3 (b). (b) Uncertainty. Consider the following simple description of faults in the brakes of a bus. Two problems may cause a brake repair to be necessary. These are a leak in the brake fluid cable, and worn brake pads. If either of these happens, one of two things may alert the driver to the problem: either noticeably reduced braking power in the bus, or an indicator light of a brake fault on the dashboard. If the driver observes either of these problems, they should take the bus to a garage for repair. Figure 2 shows the Bayesian network for modelling repairs in a bus. Nodes rep- resent the following: L for a leak in the brake cable; P for a worn brake pad; F for à fault in the brakes; R for reduced braking power; I for an indicator light of a fault on the dashboard; and G for the bus is taken to a garage for a brake repair. (i) Give an informal description of why the arrows in the diagram are neces- sary, and why the arrows which are not present may be omitted correctly. (ii) Suppose we are given the following conditional probability values for the Bayesian Network: P(L) P(F|notL, P) =0.99, P(F|L, not P) = 0.99, P(F|notL, notP) = 0.1. From these values and the diagram, calculate the value of P(F) to three decimal places 0.1, P(P) 0.2, P(F|L, P) = 0.999, %3D