document.write( "Question 1191803: A certain disease has an incidence rate of 0.9%. If the false negative rate is 4% and the false positive rate is 5%, compute the probability that a person who tests positive actually has the disease. \n" ); document.write( "

Algebra.Com's Answer #823741 by ikleyn(52832) $\"\"$ $\"About$

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\n" ); document.write( "A certain disease has an incidence rate of 0.9%.
\n" ); document.write( "If the false negative rate is 4% and the false positive rate is 5%,
\n" ); document.write( "compute the probability that a person who tests positive actually has the disease.
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\n" ); document.write( "\n" ); document.write( "My previous solution was incorrect, as tutor @math_tutor2020 noticed it.\r
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\n" ); document.write( "\n" ); document.write( "So now you see the corrected and fixed version.   Thanks to tutor @math_tutor2020.\r
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\n" ); document.write( "\n" ); document.write( "            This problem is about calculating the CONDITIONAL PROBABILITY.\r
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\n" ); document.write( "\n" ); document.write( "            They want you calculate this ratio    $\"tests_positive_AND_has_the_disease%2Ftests_positive\"$ .\r
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document.write( "Let X be the total population.\r\n" );
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document.write( "Then the number of those who has the disease is 0.009*X;  the number of those who has no the disease is 0.991*X.\r\n" );
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document.write( "     The number of those who has    the disease and tests positive is  0.009*(1-0.04)X = 0.009*0.96*X  (true  test positive)\r\n" );
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document.write( "                (to get this amount, I exclude from the sick persons, 0.009*X, the number of false negative 0.009*x*0.04.\r\n" );
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document.write( "     The number of those who has no the disease and tests positive is  0.991*0.05*X                    (false test positive).\r\n" );
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document.write( "So the number of those who tests positive is the sum  0.009*0.96*X + 0.991*0.05*X.\r\n" );
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document.write( "They want you calculate  the conditional probability\r\n" );
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document.write( "    P =  =  = cancel X in the numerator and in the denominator = \r\n" );
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document.write( "                   =  =  = use your calculator = 0.1485  (rounded).    ANSWER\r\n" );
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document.write( "ANSWER.  This probability is  0.1485.\r\n" );
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