document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151389>Question 1151389</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A diagnostic test for a certain disease is said to be 90% accurate in that, if a person has the disease, then the test will detect with probability 0.9. <BR>\n" );
document.write( "Also, if a person does not have the disease, then the test will report that he or she doesn’t have it with probability 0.9. Only 1% of the population has the disease in question. If the diagnostic test reports that a person chosen at random from the population has the disease, then what is the conditional probability that the person, in fact, has the disease? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773594 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=773594\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We are given this info:<BR>\n" );
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document.write( "Chances a person with the disease tests positive = 0.90 [GIVEN]<BR>\n" );
document.write( "Chances a person with the disease tests negative = 0.10 <BR>\n" );
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document.write( "Chances a person without the disease tests positive = 0.10 <BR>\n" );
document.write( "Chances a person without the disease tests negative = 0.90 [GIVEN]<BR>\n" );
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document.write( "It is also given that the person chosen at random tests positive for the disease, so we are only concerned with:<BR>\n" );
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document.write( "Chances a person with the disease tests positive = 0.90<BR>\n" );
document.write( "Chances a person without the disease tests positive = 0.10<BR>\n" );
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document.write( "We also know that only 1% of the population actually has the disease, so the above needs to be weighted as such:<BR>\n" );
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document.write( "Chances a person with the disease tests positive = 0.90 * 0.01 = 0.009<BR>\n" );
document.write( "Chances a person without the disease tests positive = 0.10 * 0.99 = 0.099<BR>\n" );
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document.write( "We want to find the probability that the random person who tested positive actually has the disease, so we compute that as such:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.009%2F%280.009+%2B+0.099%29 ALIGN=MIDDLE  ALT=\"0.009%2F%280.009+%2B+0.099%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.009%2F0.108 ALIGN=MIDDLE  ALT=\"0.009%2F0.108\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.0833 </SPAN>\n" );
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