A manufacturing company employs three analytical plan for the design and development of a particular product. For cost reasons, all three are used at varying times. In facts plan 1, 2, and 3 are…

A manufacturing company employs three analytical plan for the design and development of a particular product. For cost reasons, all three are used at varying times. In facts plan 1, 2, and 3 are used for 30%, 20% and 50% of the products respectively. The defect rate in different procedures is as follows: P(D/P_1) = 0.01, P(D/P_2) = 0.03, P(D/P_3) = 0.02, Where P(D/P_j) is the probability of a defective product, given plan j. If a random product was observed and found to be defective, which plan was most likely used and thus responsible?