Question: An education study gives information on the study mode (full-time or part-time) of students studying for a post-school qualification as well as their employment status. This information is summarised in the following table, expressed in percentages (%) of students enrolled in post-school education:
Employment status Studying full-time Studying part-time
Employed full-time 6.4 37.7
Employed part-time 18.1 12.2
Not employed 17.4 8.2
(a) Suppose that you select a full-time student. What is the probability that they are not employed?
(b) Suppose that you know that a student is employed full-time. What is the probability that they are studying full-time?
(c) Are the two events, 'employed full-time' and 'studying full-time', statistically independent? Explain.
(d) What is the probability that a part-time student is in full-time employment?
(e) What is the probability that a part-time student is not in full-time employment?