a. Express the joint probability distribution P(A, B, C) induced by the Bayes net in Figure S13.32 in terms of the associated conditional probability distributions.

Compute the values of the following probabilities: 

b. P(C = true). 

c. P(A = true, B = true). 

d. (A = true, B = true | C = true).

Figure S13.32

P(A=T) P(A=F) 1/4 3/4 A C B |A=T, B=T A=T, B=F A=F, B=T A=F, B=F P(B-T) P(B=F) 3/4 1/4 P(C=T|A,B) P(C=F|A,B) 1 0 0 1 1/2 0 1/2 1