Refer to Example 4. States D and G are referred to as absorbing states because a student who enters either one of these states never leaves it. Absorbing states are discussed in detail.

(A) How can absorbing states be recognized from a transition diagram? Draw a transition diagram with two states, one that is absorbing and one that is not, to illustrate.

(B) How can absorbing states be recognized from a transition matrix? Write the transition matrix for the diagram you drew in part (A) to illustrate.

Data from Example 4

Part-time students in a university MBA program are considered to be entry-level students until they complete 15 credits successfully. Then they are classified as advanced-level students and can take more advanced courses and work on the thesis required for graduation. Past records indicate that at the end of each year, 10% of the entry-level students (E) drop out of the program (D) and 30% become advanced-level students (A). Also, 10% of the advanced-level students drop out of the program and 40% graduate (G) each year. Students that graduate or drop out never return to the program.

Draw a transition diagram. 

Find the transition matrix P.

What is the probability that an entry-level student graduates within 4 years? Drops out within 4 years?