Consider the problem of detecting if an email message contains a Virus. Say we use four random variables to model this problem: Boolean class variable V indicates if the message contains a virus or not, and three Boolean feature variables: A, B and C. We decide to use a Nave Bayes Classifier to solve this problem so we create a Bayesian network with arcs from V to each of A, B and C. Their associated CPTs are created from the following data: P(V) = 0.2, P(A|V) = 0.8, P(A|V) = 0.4, P(B|V) = 0.3, P(B|V) = 0.1, P(C|V) = 0.1, P(C|V) = 0.6

(a) [4] Compute P(A, B, C | V)

(b) [4] Compute P(A, B, C)