[Maximum mark: 19] A medical centre is testing patients for a certain disease. This disease occurs in 5 % of the population. They test every patient who comes to the centre on a particular day. (a) State the sampling method being used. [1] It is intended that if a patient has the disease, they test "positive", and if a patient does not have the disease, they test "negative". However, the tests are not perfect, and only 99% of people who have the disease test positive. Also, 2 % of people who do not have the disease test positive. The tree diagram shows some of this information. 99 % test positive disease 5 % b . test negative test positive no disease d test negative (b) Write down the value of (i) a. (ii) 1;. (iii) 6. (iv) d. [4] (c) Use the tree diagram to nd the probability that a patient selected at random (i) will not have the disease and will test positive. (ii) will test negative. (iii) has the disease given that they tested negative. [8] (d) The medical centre nds the actual number of positive results in their sample is different than predicted by the tree diagram. Explain why this might be the case. [1] The staff at the medical centre looked at the care received by all visiting patients on a randomly chosen day. All the patients received at least one of these services: they had medical tests (M). were seen by a nurse (N). or were seen by a doctor (D). It was found that: - 78 had medical tests. 45 were seen by a nurse: 30 were seen by a doctor: 9 had medical tests and were seen by a doctor and a nurse: 18 had medical tests and were seen by a doctor but were not seen by a nurse: 11 patients were seen by a nurse and had medical tests but were not seen by a doctor: 2 patients were seen by a doctor without being seen by nurse and without having medical tests. (e) Draw a Venn diagram to illustrate this information. placing all relevant information on the diagram. [3] (f) Find the total number of patients who visited the centre during this day. [2]