Question

(Finite Math)

• Use Venn diagrams for survey results.
• Use survey results to complete Venn diagrams and answer questions about the survey.

1) An anonymous survey of college students was taken to determine behaviors regarding​ alcohol, cigarettes, and illegal drugs. The results were as​ follows: 869 drank alcohol​ regularly, 668 smoked​ cigarettes, 210 used illegal​ drugs, 427 drank alcohol regularly and smoked​ cigarettes, 123 drank alcohol regularly and used illegal​ drugs, 123 smoked cigarettes and used illegal​ drugs, 98 engaged in all three​ behaviors, and 278 engaged in none of these behaviors.

a) How many students were​ surveyed? _____

b) How many drank alcohol or smoked cigarettes​? _____

c) How many used illegal drugs ​only? _____

d) How many drank alcohol and smoked cigarettes​, but did not use illegal drugs​?_____

e) How many drank alcohol or used illegal drugs​, but did not smoke cigarettes​?

f) How many engaged in exactly two of these​ behaviors? ______ (Add up the values in the regions where exactly two sets intersect.)

g) How many engaged in at least one of these ​behaviors? _____  (Adding up the values in the regions of A ∪ C ∪ D)

Answer 1