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Question 5 : Bayesian Belief Networks (15 pts) Dog Barks Rains Cat Scared Cat Hides All nodes are binary and can take 0/1 values The probabilities are given below: P(Bark = 1) = 0.05 P(Rain = 1) = 0.01 P(Scared = 1 Bark = 0, Rain = 0) = 0.001 P(Scared = 1 Bark = 0, Rain = 1) = 0.1 P(Scared = 1| Bark = 1, Rain = 0) = 0.8 P(Scared = Bark = Rain = 1) = 0.9 P(Hides = 1 Scared = 1) = 0.95 P(Hides = Scared = 0) = 0.05 For the given Bayesian network, Compute the following probabilities : (a) (4 pts) Find the probability that cat hides = 1. (4 pts) Given that cat got scared (Scared = 1), what is the probability that it rained (Rain = 1)? (c ) (7 pts) Given that cat got scared (Scared = 1) and the dog barked (Bark = 1), what is the probability that it rained (Rain = 1)