Problem
Suppose you work for a company that produces chocolates. You head the quality control team and are in charge to spot chocolates that do not meet sufficient quality standards (bad chocolates). A quality control company is offering you a service to automatically spot bad chocolates. However, they declare an error of 0.5% in detecting bad chocolates when they are actually good, and a 0.6% error of detecting good chocolates when they are actually bad. Considering a sample of 10,000 chocolates, what is the probability of that a chocolate is really bad given that it has been identified by the system as bad?