3.5.5 Suppose that the items produced by a certain process are each graded as defective or good and that whether or not a particular item is defective or good depends on the quality of the previous item. To be specific, suppose that a defective item is followed by another defective item with probability 0.80, whereas a good item is followed by another good item with probability 0.95. Suppose that the initial (zeroth) item is good. Using equation (3.31), determine the probability that the eighth item is good, and verify this by computing the eighth matrix power of the transition probability matrix.