Please help me out with this question.

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 PD tue 0.2P(Bte)-0.5 P(C tme)-0.8 A BPD true | A, B) F F0.9 FTI 0.6 T?F? 0.5 TTI 0.1 FFI 0.2 FITI 0.4 T F0.8 TIT 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 PD tue 0.2P(Bte)-0.5 P(C tme)-0.8 A BPD true | A, B) F F0.9 FTI 0.6 T?F? 0.5 TTI 0.1 FFI 0.2 FITI 0.4 T F0.8 TIT 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