(10 marks) Defective items coming off an assembly line are determined to be caused by exactly...

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(10 marks) Defective items coming off an assembly line are determined to be caused by exactly one of 3 factors. For any randomly selected defective item, the probability the defect is caused by factor i is i' /36, i=1,2,3. It is also known that for any randomly selected defective item, the probability of correctly detecting it is caused by factor i upon testing for factor i is, i=1,2,3. 5 Also, there is no possibility of a false positive. For example, if the cause is due to factor 1, there is a zero probability that a test for factors 2 or 3 will result in a positive test result. a) (5 marks) For a randomly selected defective item, given a test for factor 1 was negative, what is the probability the defect is caused by factor 1? b) (5 marks) For a randomly selected defective item, given a test for factor 2 was negative, what is the probability the defect is caused by factor 3? (10 marks) Defective items coming off an assembly line are determined to be caused by exactly one of 3 factors. For any randomly selected defective item, the probability the defect is caused by factor i is i' /36, i=1,2,3. It is also known that for any randomly selected defective item, the probability of correctly detecting it is caused by factor i upon testing for factor i is, i=1,2,3. 5 Also, there is no possibility of a false positive. For example, if the cause is due to factor 1, there is a zero probability that a test for factors 2 or 3 will result in a positive test result. a) (5 marks) For a randomly selected defective item, given a test for factor 1 was negative, what is the probability the defect is caused by factor 1? b) (5 marks) For a randomly selected defective item, given a test for factor 2 was negative, what is the probability the defect is caused by factor 3?

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