A professor continually gives test to his students. He can give three possible types of test, and her class is graded as either having done well or badly. Let pi denote the probability that the class does well on a type i test, and suppose that p1=0.3, p2=0.6, and p3=0.9. If the class does well on an test, then the next test is equally likely to be any of the three types. If the class does badly, then the next test is always type 3. We are interested in the types of tests that the professor gives over time.

Define Markov Chain for this question

What proportion of the tests are type i, i=1,2,3?