an anoymous survey of college students was taken to determine behaviors regarding alcohol,cigarretes and illegal drugs 859 drank
alcohol regularly,645 smoked cigarretes, 207 use illegal drugs,397 drank alcohol regularly and smoked cigarretes,109 drank alcohol regulary and used illegal drugs ,85engaged in all three behaviors,274 engaged in none of thses behaviors
You have to use carefully Venn Diagram to solve this problem: n, here below means number of students
GIVEN ---------- n(Cigarettes) = 645 n(Alcohol) = 859 n(Drugs) = 207 n(Alcohol ∩ Cigarettes) = 397 n(Alcohol ∩ Drugs) = 109 n(Alcohol ∩ Cigarettes ∩ Drugs) = 85 And 274 Students "Clean from any of the above" Let x be the unknown number, that is n(Cigarettes ∩ Drugs) Start by drawing 3 intersecting circles, one for Alcohol, another for Cigarettes and the 3rd for Drugs:
3) n( Drugs ONLY) =207- 109 -85 - x = 13 - x (only Drugs).
(Remember that there are 274 Students clean, not shown in Venn)
Total of students (we need it to solve):
TOTAL n(STUDENT) = Alcohol Alone+ Cigarette Alone+ Drug Alone + 274 TOTAL n(STUDENT) = 268 + (163-x) + (13-x) + 274 TOTAL n(STUDENT) = 718 -2x (hope you can get the TOTAL n(STUDENT) to be able to find x, which is the n(Drugs ∩ Cigarettes)
