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
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-> 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
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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?
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
