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

Question

Each time a shopper purchases a tube of toothpaste, she chooses either brand A or brand B. Suppose that for each purchase after the first, the probability is that she will 1S choose the same brand that she chose on her preceding purchase and the probability brand B on her first purchase, what is the probability that both her first and second purchases will be brand A and both her third and fourth purchases will be brand B'? is 3 that she will switch brands. If she is equally likely to choose either brand A or

Explanation / Answer

P(both firt and second purchase brand A and third and fourth is brand B)

=P(brand A)*P(2nd brand A| first brand A)*P(3rd brand B|2nd brand A)*P(4th brand B|3rd brand B)

=(1/2)*(1/3)*(2/3)*(1/3)=1/27

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