Students at U of A have expressed dissatisfaction with the fast pace at which the math department is teaching the one-semester Cal I. To cope with this problem, the math department is now offering Cal I in 4 modules. Students will set their individual pace for each module and, when ready, will take a test that will elevate them to the next module.

The tests are given once every 4 weeks, so that a diligent student can complete all 4 modules in one semester. After a couple of years with this self-paced program, 20% of the students did not complete the first module on time. The percentages for modules 2 through 4 were 22%, 25%, and 30%, respectively.

(a) Express the problem as a Markov chain.

(b) On the average, would a student starting with module 1 at the beginning of the current semester be able to take Cal II the next semester (Cal I is a prerequisite for Cal II)?

(c) Would a student who has completed only one module last semester be able to finish Cal I by the end of the current semester?

(d) Do you recommend extending the module idea to other basic classes? Explain.