Accuracy of a Genetic Test

Consider a particular genetic disease affects 3% of adults in the U.S. population. Fortunately, there is a genetic test for the gene that causes the disease. The test is 98% accurate; that is, 98% of the people who take the test get the correct result (and 2% of people tested get the wrong result).

In Springfield, there are 100,000 adults, and they all get tested for the disease.

1. How many of the residents of Springfield are likely to have the disease?
2. How many of the people who actually have the disease get a positive test result?
3. How many of the people who do not have the disease get a positive test result?
4. Of the people who get a positive test result, how many of them have the disease? Convert this to a percentage: What percent of people who get a positive result actually have the disease?
5. What does this percentage tell you about the test?

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