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, that is, 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 that a part is scrapped in the production process.