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

[TSN79]

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...

 

[NateTG]

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?

 

[TSN79]

Well, wouldn't that be 50 and 1?

 

[NateTG]

So, how likely is a positive test to indicate disease?