In a certain country, 9% 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 2% 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 25% of a sample population tests positive. If we assume this sample is representative, what fraction of the population has the disease?