Question 1 (50 points) Consider the Car-Starting network in Figure 1. Let B = Battery, F = Fuel, G = Gauge, T = Turn Over, and $ = Start. The conditional probabilities are then given by the following: P(B = bad) = 0.02 P(F = empty) = 0.05 P(G = empty | B = good; F = not empty) = 0.04 P(G = empty | B = good; F = empty) =0.97 P(G = empty | B = bad; F = not empty) = 0.10 P(G = empty | B = bad; F = empty) = 0.99 P(T = false | B = good) = 0.03 P(T = false | B = bad) = 0.98 P(S = false | 7 = true: F = not empty) = 0.01 P(S = false | 7 = true; F = empty) = 0.92 P(S = false | 7 = false; F = not empty) = 1.00 P(S = false | 7 = false; F = empty) = 0.99 Battery Fuel Gauge Turn Over Start Figure 1: The Car-Starting network. Calculate P(F = empty | $ = no), i.e., the probability of the fuel tank being empty conditioned on the observation that the car does not start