Problem 4 [30 points]. Consider the following Bayesian network, where variables A through E are all Boolean valued: P(A-true)-0.2 PB-true)-0.5 PC-tue)-0.8 A B P(D-true | A,B) FIF FIT 0.9 0.2 TIF TIT a) [5 points] What is the probability that all five of these Boolean variables are true? Page 1 b) 10 points Compute P(A, E B) c) [5 points Compute P(A true | B-false,Cfalse, D-false, E false) d) 5 points] Compute P(C = true, D = false B-false) e) 5 points) Compute P(B-true. C false, D-true ! A false) Problem 4 [30 points]. Consider the following Bayesian network, where variables A through E are all Boolean valued: P(A-true)-0.2 PB-true)-0.5 PC-tue)-0.8 A B P(D-true | A,B) FIF FIT 0.9 0.2 TIF TIT a) [5 points] What is the probability that all five of these Boolean variables are true? Page 1 b) 10 points Compute P(A, E B) c) [5 points Compute P(A true | B-false,Cfalse, D-false, E false) d) 5 points] Compute P(C = true, D = false B-false) e) 5 points) Compute P(B-true. C false, D-true ! A false)