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 (t + 1). Consider the following probabilities:
P(A) = .8, P(B|A) = .9, and P(B|AC) = .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 P(Ac).
d. Find P(A ∩ B).
e. Find P(Ac ∩ B).
f. Use the probabilities, parts d and e, to find P1B2.
g. Use Bayes' Rule to find P(A|B), 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 (t + 1).