4. Jim must make five years worth of progress to complete his doctorate degree at ABC University. However, he enjoys the life of a student and is in no hurry to finish his degree.

In any academic year there is a 50% chance he may take the year off and a 50% chance of his pursuing the degree full time. After completing three academic years, there is a 30% chance that Jim may "bailout" and simply get a master's degree, a 20% chance of his taking the next year off but continuing in the Ph.D. program, and 50% chance of his attending school full time toward his doctorate.

(a) Express Jim's situation as a Markov chain.