Given the Bayesian network shown in Figure 4.58, compute the following probabilities:

(a) P(B = good, F = empty, G = empty, S = yes). (b) P(B = bad, F = empty, G = not empty, S = no). (c) Given that the battery is bad, compute the probability that the car will start.

P(B bad) 0.1 P(F- empty) 0.2 Battery) Fuel Gauge P(G empty I B good, F not empty) 0.1 P(G- empty I B- good, F - empty) 0.8 P(G empty I B-bad, F not empty) 0. P(G- empty I B- bad, F- empty) 0.9 Start P(S no I B-good, F not empty) 0.1 P(S no I B good, F empty) 0.8 P(S no I B bad, F not empty) 0.9 P(S no l B bad, F empty) 1.0 Figure 4.58. Bayesian network for Exercise 11