- A disease is known to be present in \(2 \%\) of a population. A test is developed to help determine whether or not someone has the disease.
Given that a person has the disease, the test is positive with probability 0.95
Given that a person does not have the disease, the test is positive with probability 0.03
- Draw a tree diagram to represent this information.
A person is selected at random from the population and tested for this disease.
- Find the probability that the test is positive.
A doctor randomly selects a person from the population and tests him for the disease. Given that the test is positive,
- find the probability that he does not have the disease.
- Comment on the usefulness of this test.