18. Given a car theft training data set which has 3 attributes/features and a class. The 3 attributes are Color, Type and Origin. The class is Stolen. Example No. Color Type Origin Stolen? 1 Red Sports Domestic Yes 234 Red Sports Domestic No Red Sports Domestic Yes Yellow Sports Domestic No Yellow Sports Imported Yes 5 6 Yellow SUV Yellow SUV Imported No Imported Yes 8 Yellow SUV Domestic No 9 Red SUV 10 Red Imported Sports Imported No Yes a) Suppose you want to build a decision tree, given the three attributes: Color, Type and Origin, what would be your choice of first root node for the decision tree you are going to build. Show your result by calculating the information gain of each attribute. b) The probabilities required for classification are listed as follows. P(Stolen Yes) = ½, P(Red | Stolen-Yes) = 3/5 P(Yellow Stolen-Yes) = 2/5 P(Sports Stolen-Yes) = 3/5 P(SUV | Stolen-Yes) = 1/5 P(Domestic | Stolen-Yes) = 2/5 P(Imported | Stolen-Yes) = 3/5 P(Stolen No) ½ P(Red | Stolen No) = 2/5 P(Yellow | Stolen = No) = 3/5 P(Sports | Stolen = No) = 2/5 P(SUV | Stolen = No) = 3/5 P(Domestic | Stolen = No) = 3/5 P(Imported | Stolen = No) = 2/5 We want to classify a {Red, SUV, Domestic}, whether the car will be stolen or not. Justify your answer using the naïve Bayesian classifier.