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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

Respuesta :

mreijepatmat
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:

1) n( Alcohol ONLY) =859-397-109-85 = 268 (only Alcohol)

2) n( Cigarettes ONLY) =645-397-85 - x= 163 - x  (only Cigarettes)

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)

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