Suppose you are a production manager for a small firm that manufactures designer phone cases. Your production facility utilizes three machines. Quality is binary each phone case is either defective or it is not defective. Each hour, Machines 1, 2, and 3 produce 10, 10 and 20 phone cases, respectively. But because the machines differ slightly in their technology, data on past production has shown that they differ in terms of their rates of defective output specifically, Machines 1, 2, and 3 have rates of defective production of 2%, 4%, and 5%, respectively.

If one phone case is selected randomly from one hour's total output, and that phone case is found to be defective, what is the probability that it was produced by Machine 1? Machine 2? Machine 3?