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4. A medical test is used to test for a certain illness. The test is 8596 accurate it 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 856 of the population have such illness. la) Find the probability that the test shows a positive resurt. (bl If the test is conducted for 10 people, nd the probability that ii) 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. [7marksl {Give the answers correct to 4 decimal places if necessary.)