document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184504>Question 1184504</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To reduce theft, a company proposes to screen the workers with a lie-detector test that has been proved  correct  90%  of  the  time  (for  guilty  subjects,  and  also  for  innocent  subjects).  The company will fire all the workers who fail the test. Suppose that 5% of workers steal from time to time.<BR>\n" );
document.write( "(a) If a worker is fired, what is the conditional probability he is innocent?<BR>\n" );
document.write( "(b) If a worker is not fired, what is the conditional probability he is guilty?Include a probability tree for this problem. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #815119 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=815119\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "(a)  P(worker innocent/lie-detector \"guilty\") = P(worker innocent ∩ lie-detector \"guilty\")/P(lie-detector \"guilty\") = 0.095/0.14 = 19/28 = 0.67857, to 5 d.p.\r<BR>\n" );
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document.write( "(b) P(worker guilty/lie-detector \"innocent\") = P(worker guilty ∩ lie-detector \"innocent\")/P(lie-detector \"innocent\") = 0.005/0.86 = 1/172 = 0.005814, to 6 d.p. </SPAN>\n" );
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