Chapter 8.7, Problem 40E

Employment You have worked for the Department of Administrative Affairs (DAA) for 27 years, and you still have little or no idea exactly what your job entails. To make your life a little more interesting, you have decided on the following course of action. Every Friday afternoon, you will use your desktop computer to generate a random digit from 0 to 9 (inclusive). If the digit is a zero, you will immediately quit your job, never to return. Otherwise, you will return to work the following Monday.

a. Use the states (1) employed by the DAA and (2) not employed by the DAA to set up a transition probability matrix P with decimal entries, and calculate $P^2\text{ and }{P}^3$.

b. What is the probability that you will still be employed by the DAA after each of the next 3 weeks?

c. What are your long-term prospects for employment at the DAA? [HinT: See Example 5.]