Confidence of feedback information for improving quality. Refer to the Engineering Applications of Artificial Intelligence (Vol. 26, 2013) study of the confidence level of feedback information generated by a semiconductor, Exercise 3.41 (p.104). Recall that at any point in time during the production process, a report can be generated indicating the system is either "OK" or "not OK". Assume that the probability of an "OK" report at one time period given an "OK" report in the previous time period is .20. Also, the probability of an "OK" report at one time period given a "not OK" report in the previous time period is .55. Now consider the results of reports generated over four consecutive time periods, where the first time period resulted in an "OK" report. Let Y represent the number of "OK" reports in the next three time periods. Derive an expression for the probability distribution of Y.