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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?

1 Answers 1