Question 1186850
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Please help me solve this question: 
Consider a shopper will choose either brand A or brand B. 
On each purchase, the probability that he will choose the same brand that he chose on his last 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?
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The key step is to understand and to write this logical expression


    P(second purchase is brand B) = P(1st purchase is brand A)*P(for 2-nd purchase switch from A to B) + 

                                  + P(1-st purchase is brand B)*P(for 2-nd purchase choose B again).



As soon as you understand it, you substitute the given values into the expression and calculate


    P(second purchase is brand B) = {{{(1/4)*(2/3)}}} + {{{(3/4)*(1/3)}}} = {{{1/6}}} + {{{1/4}}} = {{{2/12 + 3/12}}} = {{{5/12}}}.    <U>ANSWER</U>
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Solved and explained.