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4. A medical test is used to test for a certain illness. The test is 85% accurate if the patient has such illness. However, if the patient does not have such illness, the test also has a 5% probability to show a positive result. Suppose 8'56 of the population have such illness. (a) Find the probability that the test shows a positive result. (bl If the test is conducted for 10 people, nd the probability that [i] at least one of them shows a positive result; Iii) exactly two of them show positive results. given that at least one of them shows a positive result. l7marks| [Give the answers correct to 4 decimal places if necessary.)