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.
11 exam-style questions on Edexcel A Level Old Maths Probability. Each one has a worked solution and a mark scheme showing where the marks go.