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. 5% 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 C.