Answer Happy

Problem 8 - Uncertain reasoning (15 marks + 8 bonus marks) Mr James Bond takes his car to the mechanic for regular servicing. The mechanic runs a test on the car transmission. The test would return one of two values: TF or NF. If the test returns TF, it indicates that the car transmission has a major issue and needs to be replaced. If the test returns NF, it indicates that the car transmission is OK. The accuracy of the test is as follows: The probability of the test returning TF when the car transmission actually has a major issue is 0.95, and the probability of the test returning NF when the car transmission does not have any issue is 0.97. After running the test on Mr James Bond's car, the mechanic told him that the test returns TF. According to the manufacturer of Mr James Bond's car, at the age of his car, only 1 in 500 cars would have a major issue with the car transmission. 1. What is the probability that Mr James Bond's car transmission has a major issue? (15 marks) 2. (Bonus question) The cost of replacing the transmission is $2,500. If the car transmission does have a major issue and it is not replaced then it will break during driving causing the entire engine to be broken which will cost $12,000. If Mr James Bond does not replace the transmission of his car now, what is the expected cost for him? (8 bonus marks)