Transcribed Image Text: R Figure 2: The Bayesian network required for Q3 (b). (b) Uncertainty. Consider the following simple description of faults in the brakes

Transcribed Image 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