expalination

QUESTION 3 A sample of academicians was surveyed about their loyalty to the university. They were asked "If you were given an offer by another university equivalent to or slightly better than your present academic position, would you remain with the university or take the other position? The following table represents the responses of the 200 academicians in the survey which were cross-classified with their length of service with the university. Table: Loyalty of Academicians and Length of Service with The University Length of Service Total Loyalty Less than 1-5 years 6-10 years More than 1 year 10 years Would remain 10 30 5 75 120 Would not remain 25 15 10 30 80 a) Represent the information in the table as a tree diagram. (5 marks) b) What is the probability of randomly selecting an academic who is loyal (3 marks) to the university and who has more than 10 years of service? c) What is the probability of selecting an academic who would not remain (3 marks) with the university and has less than 1-year length of service? d) What is the probability of selecting an academic who would remain with (3 marks) the university, given that he or she has 1-5 years length of service? e) What is the probability of selecting an academic who would not remain (3 marks) with the university, given that he or she 6-10 years length of service? f) What is the probability of selecting an academic with more than 10 (3 marks) years of service or one who would not remain with the company? (Total:20 marks)