document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187758>Question 1187758</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a company tests its workers with a lie-detector that is correct 90% of the time and fires anyone fail the test suppose 5% of the workers are guilty of theft\r<BR>\n" );
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document.write( "1- for the workers who are fired ,calculate the percentage of them are actually guilty ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818791 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818791\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "a company tests its workers with a lie-detector that is correct 90% of the time and fires anyone <BR>\n" );
document.write( "fail the test suppose 5% of the workers are guilty of theft.<BR>\n" );
document.write( "1) for the workers who are fired, calculate the percentage of them are actually guilty ?<BR>\n" );
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document.write( "The problem seems to be tangled, &nbsp;but it is because it is &nbsp;(intently ?) &nbsp;formulated in a way<BR>\n" );
document.write( "to confuse the reader.\r<BR>\n" );
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document.write( "I will reformulate it, &nbsp;and then everything will become clear as at a sunny day.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "    a company tests its workers with a lie-detector. The device is correct in 90% cases,\r\n" );
document.write( "    which means that if it recognizes/detects  lie/theft  in  100 cases,  then in 90 cases it is right.\r\n" );
document.write( "    Let the amount of people recognized as liers is 5% of the work force.\r\n" );
document.write( "    Among this 5% people, detected as liers, what is the percentage of those who are actually guilty ?\r\n" );
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document.write( "After my re-formulation,  &nbsp;the  &nbsp;&nbsp;<U>ANSWER</U>  &nbsp;&nbsp;is as clear as &nbsp;&nbsp;2 x 2 = 4:\r<BR>\n" );
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document.write( "    90% of these 5% are actually guilty.\r\n" );
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document.write( "    Or, in other words,  0.9*0.05 = 0.045 = 4.5% of total workers are actually guilty.\r\n" );
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document.write( "Solved, &nbsp;answered and explained.\r<BR>\n" );
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document.write( "More advanced reader will notice that we are given the &nbsp;<U>conditional probability</U> \r<BR>\n" );
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document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28_lier_%29%2FP%28_detected_as_a_lier%29 ALIGN=MIDDLE  ALT=\"P%28_lier_%29%2FP%28_detected_as_a_lier%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 90% = 0.9    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(*)\r<BR>\n" );
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document.write( "and  also are given that &nbsp;&nbsp;P(detected as a lier) = 0.05.\r<BR>\n" );
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document.write( "The question is to find  &nbsp;&nbsp;P ( lier ).\r<BR>\n" );
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document.write( "Then  from &nbsp;(*),  &nbsp;we get the answer/answers formulated above.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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