document.write( "Question 1186850: 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? \n" ); document.write( "

Algebra.Com's Answer #817828 by ikleyn(52810) $\"\"$ $\"About$

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\n" ); document.write( "Please help me solve this question:
\n" ); document.write( "Consider a shopper will choose either brand A or brand B.
\n" ); document.write( "On each purchase, the probability that he will choose the same brand that he chose on his last preceding purchase is 1/3,
\n" ); document.write( "and the probability that he will switch brands is 2/3.
\n" ); document.write( "Suppose that on his first purchase the probability that he will choose brand A is 1/4
\n" ); document.write( "and the probability that he will choose brand B is 3/4.
\n" ); document.write( "What is the probability that his second purchase will be brand B?
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document.write( "The key step is to understand and to write this logical expression\r\n" );
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document.write( "    P(second purchase is brand B) = P(1st purchase is brand A)*P(for 2-nd purchase switch from A to B) + \r\n" );
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document.write( "                                  + P(1-st purchase is brand B)*P(for 2-nd purchase choose B again).\r\n" );
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document.write( "As soon as you understand it, you substitute the given values into the expression and calculate\r\n" );
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document.write( "    P(second purchase is brand B) =  +  =  +  =  = .    ANSWER\r\n" );
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