SOLUTION: Tutors A certain disease has an incidence rate of 0.5%. If the false negative rate is 7% and the false positive rate is 2%, compute the probability that a person who tests positive

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Question 1061648: Tutors A certain disease has an incidence rate of 0.5%. If the false negative rate is 7% and the false positive rate is 2%, compute the probability that a person who tests positive actually has the disease.
Found 2 solutions by Edwin McCravy, jorel1380:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
A certain disease has an incidence rate of 0.5%. If the false
negative rate is 7% and the false positive rate is 2%, compute
the probability that a person who tests positive actually has
the disease.
A lot more information is given here than we need to answer
the question.

Note that if
a person who tests positive actually has the disease.
then the positive test has succeeded.

So we are simply asked for the probability that a positive test 
succeeds.

We are told that:
The false positive rate is 2%...
That means that the probability that a positive test
fails is 2%.

Therefore the probability that a positive test
succeeds is 100% - 2% = 98%.

[The other numbers given are unnecessary to answer this, 
for they are about negative tests and what the probability
that a randomly picked person has the disease.]

Edwin
Answer by jorel1380(3719)   (Show Source): You can put this solution on YOUR website!
Consider a population of 100,000 who get the test. Of those people, .5%, or 500 people actually have the disease, but 7% will test negative, so 465 out of those 500 will test positive. Of the 99,500 who don't have the disease, 2%, or 1990 will test positive. In total, 2,455 will test positive, of which 465 will actually have the disease. So the ratio of diseased to positive tests is 465/2455 , or 0.18941. This is the probability that someone who tested positive actually has the disease. ☺☺☺☺
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