Each time a shopper purchases a tube of toothpaste, he chooses either brand a or brand b. suppose that for each purchase after the first, the probability is 1/3 that he will choose the same brand that he chose on his preceding purchase and the probability is 2/3 that he will switch brands. if he is equally likely to choose either brand a or brand b on his first purchase, what is the probability that both his first and second purchases will be brand a and both his third and fourth purchases will be brand b?