Consider a shopper will choose either brand A or brand B. On each purchase, the probability that he will choose the same brand that he chose on his last 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?