Siemens produces Diesel Generator sets in 3 manufacture plants X, Y & Z. Plant X produces 45% of the DG sets & the probability that a DG set manufactured here is defective is 2%. Plant Y produces 30% of the DG sets & the probability that a DG set manufactured here is defective is 5%. Plant Z produces 25% of the DG sets & the probability that a DG set manufactured here is defective is 1%. a) Make the probability tree for this experiment. b) If a DG set is randomly selected. What is the probability that it is defective? c) If a DG set is selected at random & found to be defective then what is the probability that it was manufactured (i) in plant X? (ii) in plant Z?