Question: The Markov chain associated with a manufacturing process may be described as follows: A part to be manufactured will begin the process by entering step 1. After step 1, 20 % of the parts must be reworked, i.e., returned to step 1, 10 % of the parts are thrown away, and 70 % proceed to step 2. After step 2, 5 % of the parts must be returned to the step 1, 10 % to step 2, 5 % are scrapped, and 80 % emerge to be sold for a profit.

(a) Formulate a four-state Markov chain with states 1, 2, 3, and 4 where 3 = a part that was scrapped and 4 = a part that was sold for a profit.

(b) Compute the probability a part is scrapped in the production process.