SOLUTION: A screening test for a disease shows a positive result in 92% of all cases when the disease is actually present and in 5% of all cases when it is not. If a result is positive, the

Question 1141848: A screening test for a disease shows a positive result in 92% of all cases when the disease is actually present and in 5% of all cases when it is not. If a result is positive, the test is repeated. Assume that the second test is independent of the first test. If the prevalence of the disease is 1 in 75 and an individual tests positive twice, what is the probability that the individual actually has the disease?

I have tried (.92/75)/(4.62/75)
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
Odds of person with disease testing positive twice: (0.92)(0.92) = 0.8464

Odds of person without disease testing positive twice: (0.05)(0.05) = 0.0025

Since the odds of a person having the disease is 1/75, we weigh the values as such:

Odds of person with disease testing positive twice: (1/75)(0.8464) = 0.01129

Odds of person without disease testing positive twice: (74/75)(0.0025) = 0.00247

Odds of person testing positive twice actually having disease: = 0.8205
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