A laboratory blood test is 99% effective in detecting a certain disease when its infection is present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1% of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?

Answer

N/a

Explanation

Let `E_(1)=` event that he has no disease,
`E_(2)=` event that he has the disease,
and `E=` event that a person is tested that imply he has a disease.
Now, `P(E_(1))=99.9/100 P(E_(2))=0.1/100`
`P(E//E_(1))=0.5/100 P(E//E_(2))=99/100`
Now `P(E_(2)//E)=(P(E_(2)).P(E//E_(2)))/(P(E_(1).P(E//E_(1))+P(E_(2)).P(E//E_(2)))`
`=(0.1/100xx99/100)/(99.9/100xx0.5/100+0.1/100xx99/100)=198/1197`