Weight defect rates by production share

A factory has three machines A,B,C producing large numbers of an item. Their shares of daily production are 50%,30%,20%, respectively.

Their respective defect rates are 2%,3%,4%. The occurrence of a defective item is independent of all other items.

One item is chosen at random from the day’s total output.

(i) Show that its probability of being defective is 0.027.

(ii) Given that it is defective, find the probability that it was produced on A.