Consider again the shopper described in Exercise 5 of Sec. 2.1. On each purchase, the probability that he will choose the same brand of toothpaste that he chose on his preceding purchase is 1/3, and the probability that he will switch brands is 2/3. Suppose that on his first purchase the probability that he will choose brand A is 1/4 and the probability that he will choose brand B is 3/4. What is the probability that his second purchase will be brand B?