Confidence of feedback information for improving quality. In the semiconductor manufacturing industry, a key to improved quality is having confidence in the feedback generated by production equipment. A study of the confidence level of feedback information was published in Engineering Applications of Artificial Intelligence (Vol. 26, 2013). At any point in time during the production process, a report can be generated. The report is classified as either “OK” or “not OK.” Let A represent the event that an “OK” report is generated in any time period (t). Let B represent the event that an “OK” report is generated in the next time period 1t + 12. Consider the following probabilities: P1A2 = .8, P1B A2 = .9, and P1B AC2 = .5.

a. Express the event B A in the words of the problem.

b. Express the event B Ac in the words of the problem.

c. Find P1Ac 2.

d. Find P1A ¨ B2.

e. Find P1Ac ¨ B2.

f. Use the probabilities, parts d and

e, to find P1B2. g. Use Bayes’ Rule to find P1A B2, i.e., the probability that an “OK” report was generated in one time period (t), given that an “OK” report is generated in the next time period 1t + 12.