Question

Suppose the A1 sauce company becomes the only sauce maker in the world, besides another new company called A2 sauce. Furthermore, suppose that with this added responsibility, both of these brands become prone to some kind of defect (cracked bottle, scratched label, spoiled sauce, etc.). Of all the bottles of A1 sauce sold, 10 percent of those have defects, and of all the bottles of A2 sauce sold, 30 percent of those have defects, and given a random bottle of sauce sold that has some kind of defect, there is a probability of 3/7 that it is A2 sauce. Given this, what proportion of all bottles sold are A2 sauce, or in other words, what is the probability that a randomly chosen bottle among all bottles sold is A2 sauce?

Answer 1