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.
Practise Edexcel A Level Old Maths Probability with exam-style questions for A Level Old Maths. 11 questions, matched to the Edexcel A Level Old Maths (9371) specification and written in Unit exams C1, C2, C3 and C4 plus two applied units (e.g. S1 and M1) style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.