The Quality Control Manager for NKA Inc

Short Answer

The quality control manager for NKA Inc. must decide whether to accept (alternative 1), further analyze (alternative 2), or reject (alternative 3) an incoming shipment (lot) of microchips. The historical data indicate that there is a 30 percent chance that the lot is poor quality (S₁), 50 percent chance that the lot is fair quality (S₂), and 20 percent chance that the lot is good quality (S₃). Assume the following payoff table is available. The values in the payoff table are in thousands of dollars.
Based on historical data, if the lot is poor quality, 40 percent of the items are defective. If the lot is fair quality, 22 percent of the items are defective. If the lot is good quality, 10 percent of the items are defective. The quality control manager inspects one unit from a recent shipment. After inspecting it, he determines that the unit is defective. Based on this additional information, determine the revised (posterior) probabilities for each of the three states of nature.