Each time that a shopper purchases a tube of toothpaste, she chooses either brand A or brand

Question:

Each time that a shopper purchases a tube of toothpaste, she chooses either brand A or brand B. Suppose that the probability is 1/3 that she will choose the same brand chosen on her previous purchase, and the probability is 2/3 that she will switch brands.
a. If her first purchase is brand A, what is the probability that her fifth purchase will be brand B?
b. If her first purchase is brand B, what is the probability that her fifth purchase will be brand B?