A laboratory blood test is `99% `effective in detecting a certain disease when it is fact 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 disease given that his test result is positive?

Explanation

Let `E_1 =` person having disease


`E'_1 =` person having no disease or healthy


`E=` result is positive, person has disease


`P(E//E_1)=99/100=0.99`


`P(E//E'_1)=0.005`


`P(E_1)=0.1/100=0.001`


`P(E'_1)=1-0.001=0.999`



To find: `P(E_1//E)`


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