Considera particular genetic disease affects 3% of adults in the U.S.population. Fortunately, there is a genetic test for the gene thatcauses the disease. The test is 98% accurate that is, 98% of thepeople who take the test get the correct result (and 2% of peopletested get the wrong result). InSpringfield, there are 100,000 adults, and they all get tested forthe disease. Howmany of the residents of Springfield are likely to have thedisease?Howmany of the people who actually have the disease get a positive testresult?Howmany of the people who do not have the disease get a positive testresult?Ofthe people who get a positive test result, how many of them have thedisease? Convert this to a percentage: What percent of people who geta positive result actually have the disease?Whatdoes this percentage tell you about the test?
100,000*0.03=3000 residents of Springfield have the disease.
3000*0.98=2940 people who actually have the disease get a positive test result.
100,000-3000=97,000 people who do not have the disease. 97,000*0.02=1940 people who do not have the disease get a positive test result.
2940+1940=4880 people who get positive test result(with and without disease). 2940/4880*100= 60.24% of people who get a positive result actually have the disease
Thispercentage tells us that the accuracy of the test must be better. 2%of wrong results in cases with big amount of tested people showthatthere are a lot of mistakes.