In a manufacturing plant, machine A produces 10% of a certain product, machine B produces 40% of this product, and machine C produces 50% of this product. Five percent of the products produced by machine A are defective, 12% of machine B product are defective, and 8% of machine C product are defective. The company inspector has just sampled a product from this plant a) What is the probability that this chosen product is defective? b) Given the chosen product is defective, what is the probability that the product is produced by machine B?