Fluorescent Penetrant Inspection (FPI) is a technique used to identify pre-existing cracks in metal components. An existing crack can lead to a premature failure in a structure that can cause the overall system to cease operating correctly. The process involves using a luminescent dye under blacklight to identify surface defects. A human inspector is responsible for performing the evaluation, and the cracks are often small and difficult to identity. Historical quality documentation shows that a trained inspector has a 98% probability of classifying a defective part correctly. It also shows that an inspector has a 4% chance of classifying a good part as defective. The overall probability of an actual defective part in a batch is 3%. For any inspection of a standard batch, the probability that a component is classified as defective and is actually defective is: