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SECTION A: TYPICAL EXAM QUESTIONS QUESTION 1: (12 MARKS) (10 MINUTES) (DoE NOV 2011) 1.1 Let A and B be two events in a sample space. Suppose that P(A) - 0,4; P(A or B) - 0, 7 and P(B) - k. 1.1.1 For what value of & are A and B mutually exclusive? (2) 1.1.2 For what value of k are A and B independent? (4) 1.2 In a random experiment it was found that; P(A) - 0,25; P(B) - 0,5 and P(A or B) - 0,625 1.2.1 Calculate P(A and B) (3) 1.2.2 Determine Jing respons, if events A and B are: (b) coinpictionary QUESTION 2: (16 MARKS) (15 MINUTES) (DOE NOV 2009) The data below was obtained from the financial aid office at a certain university. RECEIVING ONIAROTH ION FINANCIAL AID FINANCIAL AID TOTAL 4 272 3 198 1 879 731 8 120 TOTAL 6 101 1 625 2 610 10 730 2.1 Determine the probability that a student selected at random is 2.1.1 receiving financial aid. (3) 2.1.2 a postgraduate student and not receiving financial aid. (3) 2.1.3 an undergraduate student and receiving financial aid. (3) 2.1.4 not receiving financial aid given that the student is a postgraduate. (3) Are the events of being an undergraduate and receiving financial aid independent? 2.2 Show ALL relevant workings to support your answer. (4)