All welders in a factory begin as apprentices. Every year the performance of each apprentice is reviewed. Past records indicate that after each review, 10% of the apprentices are promoted to professional welder, 20% are terminated for unsatisfactory performance, and the remainder continue as apprentices.
A. Draw a transition diagram.
B. Write the transition matrix.
C. What is the probability that an apprentice is promoted to professional welder within 2 years? Within 4 years?
This is an example of a Markov chain probability problem, including transition diagram and matrix.