Suppose you are given the following set of data with three Boolean input variables a, b, and c, and a single Boolean output variable K. a bc K 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 01 For parts (a) and (b), assume we are using a naive Bayes classifier to predict the value of K from the values of the other variables. (a) [1.5 pts] According to the naive Bayes classifier, what is P(K = 1|a = 1Ab=1Ac= 0)? (b) [1.5 pts] According to the naive Bayes classifier, what is P(K = 0|a = 1 Ab= 1)? (c) [1.5 pts] According to the joint Bayes classifier, what is P(K = 1|a = 1 Ab = 1Ac= 0)? (d) [1.5 pts] According to the joint Bayes classifier, what is P(K = 0|a = 1Ab = 1)? %3D (e) [2 pts] Imagine I tell you the following: P(Z|X) = 0.7 P(Z|Y) = 0.4 Do you have enough information to compute P(Z|X AY)? If not, write "not enough info". If so, compute the value of P(Z|X AY) from the above information. (f) [2 pts] Instead, imagine I tell you the following: P(Z|X) = 0.7 P(Z]Y) = 0.4 P(X) = 0.3 P(Y) = 0.5 Do you now have enough information to compute P(Z|X AY)? If not, write "not enough info". If so, compute the value of P(Z|X AY) from the above information. (g) [2 pts] Instead, imagine I tell you the following (falsifying my earlier statements): P(Z A X) = 0.2 P(X) = 0.3 P(Y) = 1 Do you now have enough information to compute P(Z|X AY)? If not, write "not enough info". If so, compute the value of P(Z|X AY) from the above information.