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

Answer:

The answer is "0.95 and 0.5271".

Step-by-step 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)  

$p(\frac{d}{+ve}) = \frac{0.105 \times 0.95}{0.105 \times 0.95 +0.895 \times 0.10 }$

           $=\frac{0.09975}{0.09975+0.0895}\\\\=\frac{0.09975}{0.18925}\\\\= 0.5271$