document.write( "Question 1197392: A customer-service supervisor regularly conducts a survey of customer satisfaction. The results of the latest survey indicate that 8% of customers were not satisfied with the service they received at their last visit to the store. Of those who are not satisfied, only 22% return to the store within a year. Of those who are satisfied, 64% return within a year. A customer has just entered the store. In response to your question, he informs you that it is less than 1 year since his last visit to the store. What is the probability that he was satisfied with the service he received? \n" ); document.write( "
Algebra.Com's Answer #830647 by ikleyn(52834)\"\" \"About 
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\n" ); document.write( "A customer-service supervisor regularly conducts a survey of customer satisfaction.
\n" ); document.write( "The results of the latest survey indicate that 8% of customers were not satisfied
\n" ); document.write( "with the service they received at their last visit to the store.
\n" ); document.write( "Of those who are not satisfied, only 22% return to the store within a year.
\n" ); document.write( "Of those who are satisfied, 64% return within a year.
\n" ); document.write( "A customer has just entered the store. In response to your question, he informs you
\n" ); document.write( "that it is less than 1 year since his last visit to the store.
\n" ); document.write( "What is the probability that he was satisfied with the service he received?
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document.write( "They want you calculate the conditional probability\r\n" );
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document.write( "    P(a customer was satisfied with the service he received | given that he returned within a year)\r\n" );
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document.write( "This probability is the fraction, whose denominator is the number of customers\r\n" );
document.write( "that returned within a year, while the numerator is the number of customers\r\n" );
document.write( "that were satisfied AND returned within a year.\r\n" );
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document.write( "The denominator is equal to  0.08*0.22 + (1-0.08)*0.64 = 0.6064.\r\n" );
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document.write( "The numerator is (1-0.08)*0.64 = 0.5888.\r\n" );
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document.write( "The probability is this fraction/(value)  \r\n" );
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document.write( "    P = \"%28%281-0.08%29%2A0.64%29%2F%280.08%2A0.22+%2B+%281-0.08%29%2A0.64%29\" = \"0.5888%2F0.6064\" = 0.9710  (rounded).\r\n" );
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