What Is the Probability That a Positive Test Indicates Actual Disease?

AI Thread Summary
The discussion centers on calculating the probability that a person who tests positive actually has the disease, given a prevalence of 1 in 1000 and a 5% false positive rate. Participants suggest using Bayes' theorem to solve the problem. The poster attempts to define probabilities, noting that out of 1,000 tests, they expect 50 false positives and 1 true positive. This leads to the conclusion that the likelihood of a positive test indicating actual disease is low. The conversation emphasizes the importance of understanding conditional probabilities in interpreting test results.
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Homework Statement



Approx. 1/1000 has a disease, and the method of testing has a 5 % false positive rate. If a random person tests positive, what is the probability that he has the disease?

Homework Equations



I'm pretty sure Baye's theorem is the thing to use.

The Attempt at a Solution



I'm having trouble defining my probabilities. I've defined that P(sick) = 0,001 and P(not sick|+) = 0,05. But then I'm stuck...
 
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You could try the problem this way:

Let's say we test 1,000 people:
How many false positives do we expect to get?
How many real positives do we expect to get?
 
Well, wouldn't that be 50 and 1?
 
So, how likely is a positive test to indicate disease?
 

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