It is known that \(4 \%\) of a population suffer from a certain disease. When a diagnostic test is applied to a person with the disease, it gives a positive response with probability 0.98 . When the test is applied to a person who does not have the disease, it gives a positive response with probability 0.01 .
Using a tree diagram, or otherwise, show that the probability of a person who does not have the disease giving a negative response is 0.9504 .
The test is applied to a randomly selected member of the population.
Find the probability that a positive response is obtained.
Given that a positive response is obtained, find the probability that the person has the disease.