Consider a machine that can be used for another year. The question has arisen as to whether the machine should be overhauled. The cost to overhaul the machine is $5000 if it is done before the machine fails but if the machine fails while in operation, it will cost $8000. Your engineers have estimated the probability that the machine will fail while in operation. You are very apprehensive since in addition to the extra cost to replace the machine, which is easily quantifiable, other problems will also arise if the machine fails while in operation that you cannot completely quantify. You would prefer to avoid being in that situation if possible. You have been told that a test can be performed on the machine to help you predict if the machine will fail in the next year. As with any test, it is imperfect, but you want to at least consider it. I have put together the decision tree that can be found attached. Screen Fail means that the screen predicts that the machine will fail. This is considered a positive test. Screen No Fail means that the screen predicts that the machine will not fail. This is considered a negative test. Please use the decision tree to answer the following questions: (Enter as percentages rounded to the nearest whole number)

2. What is the probability that the test will predict that the machine will fail? [B]

Overhaul ' 5 (5,000.00) $ (5,000.00) Do we overhaul? No Screen 5 [ (4,800.00) Fail 60.0% ' 5 (8,000.00) 5 (8,000.00) N o Overhaul 5 (4,800.00) 40.0% Ma Fail ' 0 $0.00 Do we 5: reen ?