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4. [9 marks] A team of researchers conducted a survey to quantify the extent, and to measure student perception, of alcohol and tobacco use Out of all students at one university, 15% smoke cigarettes, 81% consume alcohol, and 9% smoke cigaretes and consume alcohol. Let C represent the event a student smokes cigarettes, and A represent the event a student consumes alcohol. Therefore P(C) = 0.15 and P(4) = 0.81. Note: For each part of this question, you must first express each probability in terms of the events C and A, and justify any computation through the use of an explicitly stated formula. You may draw a Venn diagram when helpful but it is not a sufficient explanation on its own. (a) As stated above, 9% of all students at the university smoke cigarettes and consume alcohol. Write this as a probability involving the events C and A. (b) Are smoking cigarettes and consuming alcohol mutually exclusive events? Explain using one or more of the three probabilities given above. (c) Are smoking cigarettes and consuming alcohol independent events? Explain using one or more of the three probabilities given above. (d) What is the probability that a student does not smoke cigarettes? (e) What proportion of all students engage in at least one of these two behaviours? (f) What is the probability that a student smokes cigarettes but does not consume alcohol