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Problem 3. (adapted from Upton and Cook, 1998, 4g.11) The academic staff employed by a college are classified as academic, administrative or support. The following table shows the numbers employed in these categories and their gender: Male Female Total Academic 42 28 70 Administrative 7 13 20 Support 26 9 35 Total 75 50 125 A member of staff is selected at random. 2 A is the event that the person selected is female; B is the event that the person selected is academic staff; C is the event that the person selected is administrative staff. ( A is the event not A, B is the event not B, C is the event not C) Write down the values of: (i) P(A); (ii) P(An B); (iii) P(AUC); (iv) P(A | C)