A factory has a machine shop in which three machines (A, B, C)produce 100cm aluminum tubes. An inspector is equally likely to sample tubes from A and B, and three times as likely toselect tubes from C as he is from B. The defective rates from the three machines are: A 10% B 10% C 20% What is the probability that a tube selected by the inspector: i. Is from machine A? ii. Is defective? iii. Comes from machine A, given that it is defective? [10 marks]