n a certain country, 5% of the population have a certain disease. A diagnostic b

Question

n a certain country, 5% of the population have a certain disease. A diagnostic blood test has been developed for the disease. If a person has the disease, the result is positive 99% of the time while if he doesn't has the disease, the result is positive 4% of the time.

If a person gets a positive blood test, what is the probability that he has the disease?

The same test is used in another country, and it is found that 16% of a sample population tests positive. If we assume this sample is representative, what fraction of the population has the disease?

Explanation / Answer

1)P(positive blood test) =P(have disease and  positive blood test+does not have disaese and  positive blood test)

=0.05*0.99+(1-0.05)*0.04 =0.0875

threfore probability that he has the disease given positive blood test

=P(have disease and  positive blood test)/P(positive blood test) =0.05*0.99/0.0875 =0.5657

2)

let x is fraction of the population has the disease

therefore P(positive blood test) =x*0.99+(1-x)*0.04 =0.16

x*0.95 =0.12

x =0.12/0.95 =0.1263

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