- #1

laura_a

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## Homework Statement

Can someone please check my answers for this probability question about disease testing (negative/positives)?

I will write the question on about below will write my answers, I would appreciate anyone letting me know if I'm right/wrong. Thanks

Q. A test for a disease has a false negative rate of 5%, false positive rate of 15%. The prevalance of the disease is 1.8%

b) if the popluation were screened, what proportion will test negative to disease

c) what proportion of those testing negative will actually HAVE the disease

d) explain why this proportion is so small

## The Attempt at a Solution

b) P(not disease) U P(false neg)

P(Disease) = 18/1000

P(not disease) = 982/1000

p(false neg) = 5/100

P (not D) U (false neg) = 982/1000 + 5/100 - (982/1000 * 5/100)

= 9829/10,000

This means 9829/10000 or 98.29% will test negative

c) how many of these actually have the disease... well I assume it is just 5% of that number because the given details say 5% test false neg.. so 5% * 98.29 = 4.91%

d) the proportion is 5% of just under 100 so that is why it is lower than the given 5% ?? not sure about d)