Question

Consider a common disorder, which we will call Z, that affects 18% of adults (18 years and over) in the U.S. Fortunately, there is a genetic screening test for the gene that causes disorder Z. 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 Johnsonville, the adult population is 150,000 and all the residents get tested for the gene linked to disorder Z.

1. How many of the residents of Johnsonville 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 test results

actually have the disease?

5. Compare your results with the problem you solved in the discussion activity (M8D1).

Specifically, focus on the percent of people who get a positive result that actually have

the disease. Remember that both genetic tests were 98% accurate. Why were the

percentages so different? Do you think the rarity of the disease affects testing results?

Why or why not? Be sure to explain your reasoning mathematically.

Answer 1

In the above question, we are given that probabiity of disorder in adults , P(Z) =0.18

Let event that test of Z is accurate be denoted by T.

Then P(Z|T) = 0.98

Adult population N = 150,000

We are asked the following probabilities

1. Residents of Johnville likely to have a disease:

  

  

In Johnville, residents likely to have disease are 27000

2. Number of people actually having disease and get a positive result

  

Required number of people is 26460

3. Number of people not having disease and test positive

  

  

4. Of the people who tested positive, people ho actually have the disease are 26240.

P(Z|T)= 0.98

Percentage = 0.98*100 = 98%