document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197392>Question 1197392</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830659 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=830659\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The other tutors approach this problem using conditional probability, and the law of total probability. <BR>\n" );
document.write( "Such methods are fine if you understand how the formula works. And it's useful for exam settings where time is important.\r<BR>\n" );
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document.write( "I'll approach this using a different method.\r<BR>\n" );
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document.write( "Let's say 10,000 people were surveyed. <BR>\n" );
document.write( "Feel free to change this number to any positive integer you want. <BR>\n" );
document.write( "I selected this large value so that the resulting values in the table below are all integers.\r<BR>\n" );
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document.write( "We're told that \"<font color=blue>8% of customers were not satisfied</font>\"<BR>\n" );
document.write( "8% of 10,000 = 0.08*10,000 = 800 people weren't satisfied.<BR>\n" );
document.write( "This means 10,000 - 800 = 9200 people were satisfied.\r<BR>\n" );
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document.write( "Another fact is \"<font color=blue>Of those who are not satisfied, only 22% return to the store within a year</font>\"<BR>\n" );
document.write( "Of the 800 unsatisfied people, 0.22*800 = 176 return to the store within a year, and 800-176 = 624 do not return within a year.\r<BR>\n" );
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document.write( "We're also told that \"<font color=blue>Of those who are satisfied, 64% return within a year</font>\"<BR>\n" );
document.write( "64% of those 9200 people satisfied = 0.64*9200 = 5888 satisfied people return within a year. The other 9200-5888 = 3312 satisfied customers do not return within a year.\r<BR>\n" );
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document.write( "Here's a table to keep track of all the values mentioned so far.<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD ></TD><TD >Satisfied</TD><TD >Not Satisfied</TD><TD >Total</TD></tr><tr><TD >Return</TD><TD >5888</TD><TD >176</TD><TD >6064</TD></tr><tr><TD >No return</TD><TD >3312</TD><TD >624</TD><TD >3936</TD></tr><tr><TD >Total</TD><TD >9200</TD><TD >800</TD><TD >10,000</TD></tr>\n" );
document.write( "</TABLE>\"Return\" of course refers to \"Return within 1 year\".\r<BR>\n" );
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document.write( "Let's move onto the part that says \"<font color=blue>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</font>\"\r<BR>\n" );
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document.write( "This means we focus entirely on the \"Return\" row.<BR>\n" );
document.write( "There are 5888+176 = 6064 people who returned within a year of their last visit.\r<BR>\n" );
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document.write( "Of those 6064 people, 5888 were satisfied.<BR>\n" );
document.write( "Divide those values to get<BR>\n" );
document.write( "5888/6064 = 0.97097625329816 approximately<BR>\n" );
document.write( "which when rounding to five decimal places we get 0.97098<BR>\n" );
document.write( "However, if your teacher needs you to round to some other level of precision, then be sure to do so.\r<BR>\n" );
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document.write( "Normally I would go with the fraction form since it's exact and avoids rounding error. <BR>\n" );
document.write( "But it's a bit tricky to visualize 5888/6064 in my opinion. <BR>\n" );
document.write( "It's much easier to grasp what 0.97098 means (about 97.098% of the people who return within a year are satisfied customers).\r<BR>\n" );
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document.write( "Answer: <font color=red>Approximately 0.97098</font><BR>\n" );
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