document.write( "Question 1207328: A certain disease has an incidence rate of 0.8%. If the false negative rate is 6% and the false positive rate is 2%, compute the probability that a person who tests positive actually has the disease. \n" ); document.write( "

Algebra.Com's Answer #845150 by math_tutor2020(3817) $\"\"$ $\"About$

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\n" ); document.write( "Terms to know:

Positive = the test claims the person has the disease (the test's claim may be true or false)
Negative = the test claims the person does NOT have the disease (the test's claim may be true or false)
False negative = when the test says \"negative\", but the person actually has the disease
False positive = when the test says \"positive\", but the person does NOT actually have the disease

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\n" ); document.write( "\n" ); document.write( "Here's a chart to help remember
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	Tests Positive	Tests Negative
Has Disease	Correct Outcome	False Negative
Does Not Have Disease	False Positive	Correct Outcome

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\n" ); document.write( "\n" ); document.write( "Consider a population of 100,000 people.\r
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\n" ); document.write( "\n" ); document.write( "\"A certain disease has an incidence rate of 0.8%\" will mean that:
\n" ); document.write( "0.8% of 100,000 = (0.8/100)*100000 = 800 people have the disease.
\n" ); document.write( "The remaining 100000 - 800 = 99,200 people do not have the disease.\r
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\n" ); document.write( "\n" ); document.write( "We are told that \"the false negative rate is 6%\".
\n" ); document.write( "Of the 800 people who have the disease, 6% of them will get a false negative.
\n" ); document.write( "The test mistakenly says to these unfortunate people \"no you don't have the disease\" when it should say \"yes you do have the disease\".
\n" ); document.write( "6% of 800 = 0.06*800 = 48 people will get a false negative when it should say \"positive\".
\n" ); document.write( "The other 800-48 = 752 people with the disease get the proper positive test result.\r
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\n" ); document.write( "\n" ); document.write( "We are also told that \"the false positive rate is 2%\"
\n" ); document.write( "It means 2% of the 99,200 people who do not have the disease, will get back erroneous results of \"positive\" when instead it should say \"negative\".
\n" ); document.write( "2% of 99200 = 0.02*99200 = 1984 people will get false positives and 99200 - 1984 = 97216 people will get correct negative test results.\r
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\n" ); document.write( "\n" ); document.write( "Here's a chart summarizing the values.
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	Tests Positive	Tests Negative	Total
Has Disease	752	48	800
Does Not Have Disease	1984	97,216	99,200
Total	2736	97,264	100,000

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\n" ); document.write( "\n" ); document.write( "Based on the chart, there are 2736 people who tested positive.
\n" ); document.write( "Of this subgroup, 752 have the disease.
\n" ); document.write( "752/2736 = 0.27485380117 is the approximate probability of someone actually having the disease if they test positive.
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