SOLUTION: A certain disease has an incidence rate of 0.7%. (This is percent of people in the population who have the disease.) The false negative rate is 5%; this is the percent of people wh

Question 1084491: A certain disease has an incidence rate of 0.7%. (This is percent of people in the population who have the disease.) The false negative rate is 5%; this is the percent of people who really have the disease, but test negative for it. The false positive rate is 3%; this is the percent of people who do not have the disease, but who test positive for it. Compute the probability that a person who tests positive actually has the disease.

Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
Consider a population sample of 100000 subjects. This means that of all these people, 100000x.007, or 700 people will actually have the disease. Of these, 95% will test negative, giving us 665 positive tests. Of the 999,300 who don't have the disease, 3%, or 2979 will test positive. So, the total of people who have the disease and test positive plus the 2979 who test positive, but DO NOT actually have the disease is 665+2979, or 3644. The ratio of people who actually have the disease to the ratio of those who test positive for the disease is 665/3644, or 0.18249176728869374313940724478595, or about 18%. ☺☺☺☺
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