In the following problem:
The probability that a shopper 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 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.
I have the following probabilities:
P(A) = 1/4 P(B) = 3/4
P(A | A) or P(B | B) = 1/3
P(A | B) or P(B | A) = 3/4
So the probability that he will choose brand B on his second purchase is:
P(A) * P(B|A) + P(B) * P(B|B) = 1/4 * 3/4 + 3/4 * 1/3
Is this correct?