Three manufacturers (Acme,Binford and Craftsmen) make the same product with the following rates:
Acme produces 40% of the total output with a non-defective ratio of 0.85
Binford produces 35% of the total output with a non-defective ratio of 0.90;
Craftsmen produces 25% of the total output with a non-defective ratio of 0.95.
A customer receives a defective product. What is the probability that it came from Binford? What assumptions did you make to answer this question?