(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?