A factory has a machine shop in which three machines (A, B, and C) each produce 100 cm aluminum tubes. An inspector is equally likely to sample tubes from from A and B and three times as likely as to select from C as he is from B. The defective rates from machine A, B and C are 10%, 10% and 20% respectively.
The probability that a tube is selected by the inspector from machine A is 1/5 = 0.2` `
The probability that a tube selected by the inspector is defective is 0.1*0.2 + 0.1*0.2 + 0.2*0.6 = 0.16
The probability that a tube is selected from A given that it is defective is P(it is from A and defective)/(probability that it is defective) = (0.2*0.1)/(0.16) = 0.125