4. [9 marks] A team of researchers conducted a survey to quantify the extent, and to measure student perception, of alco

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4 9 Marks A Team Of Researchers Conducted A Survey To Quantify The Extent And To Measure Student Perception Of Alco 1 (70.54 KiB) Viewed 110 times

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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 cigarettes and consume alcohol. Let Crepresent the event a student smokes cigarettes, and A represent the event a student consumes alcohol. Therefore P(C)= 0.15 and P(A) = 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 а 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 and A. (b) Are smoking cigarettes and consuming alcohol mutually exclusive events? Explain using one or more of the three probabilities given above.