Parts and Materials for the skis made by the Downhill Adventures Company are supplied by two suppliers. Supplier A's materials make up 30% of what is used, with supplier B providing the rest. Past records indicate that 15% of supplier A's materials are defective and 10% of B's are defective. Since it is impossible to tell which supplier the materials came from once they are in inventory, the manager wants to know which supplier most likely supplied the defective materials the foreman has brought to his attention. Provide the manager this information.
A) Supplier A
B) Supplier B
C) Both are equally likely
D) Cannot be determined from this information

Question

Quizplus · Accepted Answer

Given that Supplier A provides 30% of the materials and has a 15% defect rate, while Supplier B provides 70% of the materials with a 10% defect rate, we can calculate the overall probability of a defective part coming from either supplier using Bayes' theorem or a weighted average. The probability that a defective part came from Supplier B is higher because they supply a larger proportion of the materials, even though their defect rate is lower than Supplier A's.

Parts and Materials for the Skis Made by the Downhill