briefly explain please

2. (a) The staffs employed by an university are classied as academic, administrative or supporting. The following table shows the numbers employed in these categories -- m- and their gender. Given that 85% of academic staff own cars, as do 70% of administrative staff and 20% of supporting staff. i. A member of staff is selected at random. Let A be the event that the person selected is female, B be the event that the person selected is an academic staff and C' be the event that the person selected is an administrative staff. Evaluate P(A U C") and PMIC). (4 marks) ii. What is the probability that a staff member selected at random owns a car? (3 marks) iii. A staff member is selected at random and found to own a car. What is the probability that this person is a member of supporting staff? (4 marks) (b) Five people are sitting at a table in a restaurant. Two of them order coffee and the other three order tea. The waiter forgot who ordered what and puts the drinks in a random order for the ve persons. Specify an appropriate sample space and determine the probability that each person gets the correct drink. (3 marks) (c) How many different sets of four letters can be formed from the word TRIANGLE if we want at least one vowel. (3 marks) (cl) In a department store, there are 50 male and 20 female salespeople. There are 45 2 junior salespeople and the others are senior. Among those junior salespeople, g of them are male. Suppose one salesperson is selected at random. i. What is the probability that the selected salesperson is a senior if a male is being selected? (3 marks) ii. Is the grade independent with the gender? Why