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

Step-by-step explanation:

Let the required probability be denoted by P(1A 2A 3B 4B).

This means a shopper chooses brand A first. Then by choosing brand A as the second purchase, the same brand is used. The third purchase is brand B; hence he switches brand. The fourth purchase is also brand B, maintaining the same brand as the third.

On the first purchase, the probabilities of A and B are both equal. Hence, each probability = 1/2

      2

  2 is to go somewhat to the top right of a because it is squared    

v= a h/3