Question
If the probability of a false positive of a medical test (could be COVID-19) is 3%, what percent of people who test positive would actually have it?
Scenario 1: The disease is present in 1 person in 1000
Scenario 2: the disease is present in 1 person in 5
Answer
Scenario 1: 3.2% and Scenario 2: 89.3%
We need to compare the actual positives with the sum of the true positives and false positives. In Scenario 1, if 1 in 1000 (.001) have it then 999 out of 1000 (.999) do not.
In Scenario 2, if 1 in 5 (.2) have it then 4 out of 5 (.8) do not.
Scenario 1:
comparing the true positives with the total positives (true positive plus false positive)
approximately 3.2%.
Scenario 2:
comparing the true positives with the total positives (true positive plus false positive)
approximately 89%
Math Confidence by Robin the Math Lady 