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Question 2 [Iotal 1o marksl T: Q [3} lb} In a university department, a head and an associate head are to be chosen from [5D - T} professors {including Professors A. B, C and D}. How many different choices of head and associate head are possible if [ii professors A and B will serve together or not at all? [2 marks} [ii} professors E and D will not serve together? [2 marks} Suppose a Medical Test has been designed to detect if a patient has infected with a certain virus. Past statistics indicate that only 5% of patients have been infected with this virus. or those patients who are not infected. about 3% of them would give a positive test result. However, about 92% of patients who are infected with the virus would give a positive test result. Suppose a patient is randomly selected. Let v be the event that the selected patient has infected with the virus. Let T be the event that the selected patient has a positive test result. [Correct your nai answers to 4 decima! places} [i} What is the probability that the selected patient was actually infected with the virus if that patient has just got a negative result from the Medical Test? [3 marks} [ii] Are the two events v and T independent? Explain with calculation. [3 marks}