15. Each time a shopper purchases a tube of toothpaste, he chooses either brand A or brand B. On each purchase, the probability that he will choose the same brand of toothpaste that he chose on his...

Extracted text: 15. Each time a shopper purchases a tube of toothpaste, he chooses either brand A or brand B. 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 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 the second purchase will be brand B?