Question

Studies indicate that 10.5% of the US population has diabetes. A producer of medical devices is developing a test for diabetes diagnosis: a positive test suggests that a person has diabetes, a negative test suggests that a person does not have diabetes. However, medical tests can give false results: in particular, the probability that this test gives a negative result for a person who actually has diabetes is 0.05, while the probability that the test is positive for a person who in fact does not have diabetes is 0.10.1. What is the probability that the test gives a positive result for a person who is known to have diabetes? 2. What is the probability that a person has diabetes, given that the test gives a positive result?

Answer 1

The answer is "0.95 and 0.5271".

Explanation:

`p (d) = 0.905 \\\\p( false\ negative) = 0.05\\\\p(false \ positive ) = 0.10 \\\\`

In point a)

p ( positive diabetes )
`= 1 - 0.05 = 0.95`

In point b)

`p((d)/(+ve)) = (0.105 * 0.95)/(0.105 * 0.95 +0.895 * 0.10 )`

`=(0.09975)/(0.09975+0.0895)\\\\=(0.09975)/(0.18925)\\\\= 0.5271`