Question: A certain reliability defect can be detected only with a destructive test. However, quality control has developed a nondestructive test that a product with the defect will fail 95% of the time. Those without the defect pass the test 95% of the time. Quality control proposes using the test as a 100% screening on all of the products. Products that fail the screening will not be replaced.

? If 2% of the product has the defect, what will be the percent of defective products that will get passed the screening?

o First, construct a table of the form below for listing all the possible probabilities, where intersections, such as P(F) and P(D) are found by finding P(F|D) * P(D), and so on.

o Note: P(F) gives the probability of failure of the screening, P(F’) is the probability of not failing the screening, P(D) is probability the product is defective, and P(D’) is the probability that the product is not defective. Remember that the probabilities must sum to 1 in the bottom-right corner.