Example: Central State University administers computer competency examinations every year. These exams allow students to test out of the introductory computer class held at the university. Results of the exams can be placed in one of the following four states: State 1: pass all of the computer exams and be exempt from the course State 2: do not pass all of the computer exams on the third attempt and be required to take the course State 3: fail the computer exams on the first attempt State 4: fail the computer exams on the second attempt The course coordinator for the exams has noticed the following matrix of transition probabilities: P 1 o 0 0 0 1 0 0 0.7 0 0.2 0.1 0.4 0.2 0.2 0.2 Currently, there are 200 students who did not pass all of the exams on the first attempt. In addition, there are 50 students who did not pass on the second attempt. In the long run, how many students will be exempted from the course by passing the exams? How many of the 250 students will be required to take the computer course? 14-17 A study of accounts receivable at the A&W Department Store indicates that bills are current 1 month overdue. 2 months overclue written olas bad dobis, or paid in full . Of those that are current. 80% are paid that month, and the rest become 1 month overdue. Of the 1 month-overdue bills, 90% are paid, and the rest become 2 months overdue. Those that are 2 months overdue will either be paid (85%) or be listed as bad debts. If the sales cach month average $150,000, determine how much the company expects to receive of this amount. How much will become bad debts? Paid Bad debt current 1 month 2 months Paid 1 0 0 0 0 Bad debt 0 1 0 0 0 pcurrent 08 0 0 02 0 I month 09 0 0 0 0.1 2 months 0.15 0 0 Festablish, & A!!! 110 1-0 1 0 lo 01 TO 0.2 Blo 0.85 0 0 0 0 0.1 0 o 10 0.8 0 A 0.9 0 10.85 0.151 0.997 0.003 FA = (0.985 0.015) 0.850 0.150 This means that 99.7% of the current bills will be paid, and 0.3% of these will be bad debts. Thus, 0.997(150.000) = $149,550 will be paid, and 0.003(150,000) = $450 will eventually become a b bad debt