Problem 1 (10 points): Consider the following Bayesian network, where variables A through E are all Boolean valued Note: there is a typo in the image, it should be P(A- true) - 0.2 instead of P(D- true) - 0.2 P(C tue) 0.8 A | B | PD=true l A, B) F F0.9 FITI 0.6 TF| 0.5 TTI 0.1 B | C | PE=true ! B. C) FFI 0.2 FITI 0.4 TFI 0.8 Ti 0.3 a) What is the probability that all five of these Boolean variables are simultaneously true? [Hint: You have to compute the joint probability distribution. The structure of the Bayesian network suggests how the joint probability distribution is decomposed to the conditional probabilities available.] b) What is the probability that all five of these Boolean variables are simultaneously false? Hint: Answer similarly to above.] c) What is the probability that A is false given that the four other variables are all known to be true? Problem 1 (10 points): Consider the following Bayesian network, where variables A through E are all Boolean valued Note: there is a typo in the image, it should be P(A- true) - 0.2 instead of P(D- true) - 0.2 P(C tue) 0.8 A | B | PD=true l A, B) F F0.9 FITI 0.6 TF| 0.5 TTI 0.1 B | C | PE=true ! B. C) FFI 0.2 FITI 0.4 TFI 0.8 Ti 0.3 a) What is the probability that all five of these Boolean variables are simultaneously true? [Hint: You have to compute the joint probability distribution. The structure of the Bayesian network suggests how the joint probability distribution is decomposed to the conditional probabilities available.] b) What is the probability that all five of these Boolean variables are simultaneously false? Hint: Answer similarly to above.] c) What is the probability that A is false given that the four other variables are all known to be true