Imagine there is a town with 10,000 people. All of them get a test for disease X
ID: 255284 • Letter: I
Question
Imagine there is a town with 10,000 people.
All of them get a test for disease X.
The 1% of the people actually have disease X.
The false positive rate for the disease is 5%.
3A. How many people in the town have the disease?
3B. How many don't have the disease?
3C. How many people who don't have the disease still get a positive test result?
3D. How many people in total got a positive test result?
3E. Maria lives in this town and got a positive test result. What is the probability that
she actually has the disease?
3F Bonus question. Mark also lives in the same town, but he is the only person in the
town who didn't get a test done. What do you think is the probability that he has the
disease?
Explanation / Answer
Total people in the town = 10000
1% of them actually have the disease X
False positive result is seen in 5% of people
3A. The number of people in the town have the disease = (10000 X 1)/100 = 100
3B. The number of people don't have the disease = (10000 - 100) = 9900
3C. The number of people who don't have the disease but showing positive result = (10000 X 5)/100 = 500
3D. The total positive result is shown both by the diseased as well as the false positive result showing people. So, the total false positive result is shown by (100+500) = 600 people.
3E. Out of 600 positive result showing people, 100 people have the disease. So, the probability of Maria for having the disease = (100/600) = 1/6 = 0.17
1F. Mark, don't know if he is diseased or not. So the probability of Mark for having the disease = (100/10000) = 1/100 = 0.01