document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165956>Question 1165956</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It is estimated that approximately 8.43% Americans are afflicted with diabetes. Suppose that a certain diagnostic evaluation for diabetes will correctly diagnose 98% of all adults over 40 with diabetes as having the disease and incorrectly diagnoses 2.5% of all adults over 40 without diabetes as having the disease.\r<BR>\n" );
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document.write( "    a) Find the probability that a randomly selected adult over 40 does not have diabetes, and is diagnosed as having diabetes (such diagnoses are called \"false positives\").\r<BR>\n" );
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document.write( "    b) Find the probability that a randomly selected adult of 40 is diagnosed as not having diabetes.\r<BR>\n" );
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document.write( "    c) Find the probability that a randomly selected adult over 40 actually has diabetes, given that he/she is diagnosed as not having diabetes (such diagnoses are called \"false negatives\").\r<BR>\n" );
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document.write( "(Note: it will be helpful to first draw an appropriate tree diagram modeling the situation) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #790410 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=790410\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look at 10000 people<BR>\n" );
document.write( "843 have diabetes\r<BR>\n" );
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document.write( "======Test+======Test-=====Total<BR>\n" );
document.write( "DM ---     826.14----  16.86 -----   843   The 98% is applied to here for test +<BR>\n" );
document.write( "Not DM=228.92===8928.08 ====9157   The 97.5 is applied here for test- (or 2.5% for test +)<BR>\n" );
document.write( "Total   --1055.06     8944.94.       10000\r<BR>\n" );
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document.write( "a.False positive is 228.92/1055.06=21.7%<BR>\n" );
document.write( "b. That is 91.57%<BR>\n" );
document.write( "c. Diagnosed as not having is 8944.94 and actually having it is 16.86, so the probability is 16.86/8944.94, or 0.00195 or 0.2% </SPAN>\n" );
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