1. The "ABC" Company has two production facilities, one in Michigan and one in Georgia. The company makes the same type of tile at both facilities. The Michigan plant makes 60% of the company's total tile output and the Georgia plant 40%. All tiles fromthe two facilities are sent to regional warehouses, where they are intermingled. After extensive study, the quality assurance manager has determined that 5% of the tiles produced in Michigan and 10% of the tiles produced inGeorgiaareunusableduetoqualityproblems.Whenthecompanysellsadefectivetile,itincurs not only the cost of replacing the item but also the loss of good-will. The vice president for production wouldliketo allocate these costs fairlybetween thetwo plants.To doso, heknows he must first determine the probability that a defective tile was produced by a particular production line. Specifically, what is the probability that the tile was produced at the Michigan plant, given that the tile is defective? Show all work. In other words, answer the following questions:
   1. Definethe event(s).
   2. Whatdowe know?
   3. Whatistheoverallprobabilityofadefectivetile?Inotherwords,whatis P(Defective)?
   4. What is the probability that the tile was produced at the Michigan plant, given that the tile is defective?
   5. Interprettheresultinpartd.