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 machine A products are defective, 12% of machine B products are defective,
and 8% of machine C products are defective. The company inspector has just sampled a
product from this plant and has found it to be defective. Determine the revised
probabilities that the sampled product was produced by machine A, machine B, or
machine C.