Chapter 9.1, Problem 4MP

Refer to Example $4$. At the end of each year the faculty examines the progress that each advanced-level student has made on the required thesis. Past records indicate that $30\%$ of advanced-level students $\left(A\right)$ complete the thesis requirement $\left(C\right)$ and $10\%$ are dropped from the program for insufficient progress $\left(D\right),$ never to return. The remaining students continue to work on their theses.

(A) Draw a transition diagram.

(B) Find the transition matrix $P$.

(C) What is the probability that an advanced-level student completes the thesis requirement within $4$ years? Is dropped from the program for insufficient progress within $4$ years?