probabiliy question . help

Question

5% of the population has X disease. A screening test accurately detects the disease for 80% of the people who actually do have it. The test also incorrectly indicates the disease for 30% of the people who actually don't have it. Suppose a randomly selected person screened for the disease tests postive. What is the probability that they have the disease?

Answer 1

Hi Joe

         The best way to calculate the chance that one has the disease after testing positive is to imagine a sample of say 1000 people randomly drawn from the population then there would be 50 (5%) people with the disease and 40 of them (80%) would test positive. Now of the 950 (1000-50) who do not have the disease 950x.3 (30%) or 285 will also test positive. Now the probability that you have the disease given that you tested positive is 40/(285+40) = .123 or 12.3% which also means that the probability that you do not have the disease is 87.7% or 7 to 1 against you having the disease. No need to get concerned.

 

Hope this helps

jim