Question

1250 people were surveyed and 911 drank alcohol or used illegal drugs. How many drank alcohol only?

Answer 1

Given:

The number of students who drank alcohol is 836 students.

`n(A)=836`

The number of students who smoked cigarettes is 624 students.

`n(C)=624`

The number of students who used illegal drugs is 176 students.

`n(D)=176`

The number of students who drank alcohol and used smoked cigarettes is 395.

`n(A\cap C)=395`

The number of students who drank alcohol and used illegal drugs is 101

`n(A\cap D)=101`

The number of students who smoked cigarettes and used illegal drugs is 106

`n(C\cap D)=106`

The number of students engaged in all three is 85.

`n(A\cap C\cap D)=85`

The total number of students is 1250 students.

`n(A\cup C\cup D)=1250-131=1119`

131 engaged in none of the behavior.

The number of students who drank alcohol or used illegal drugs is 911

`n(AUD)=911`

Required:

We need to find the number of students who drank alcohol only.

Step-by-step explanation:

Let set A represents the number of students who drank alcohol.

Let set C represents the number of students who smoked cigarettes.

Let set D represents the number of students who used illegal drugs.

Consider the formula.

`n(A\cup C\cup D)=n(A)+n(C)+n(D)-n(A\cap C)-n(A\cap D)-n(C\cap D)-n(A\cap C\cap D)`

`n(AUD)=911`

`n(A\text{ only\rparen=n\lparen A\rparen-}n(A\cap D)-n(A\cap C)+n(A\cap C\cap D)`

Substitute know values.

`n(A\text{ only\rparen=836-395-101+85}`
`n(A\text{ only\rparen=425}`

Final answer:

The number of students who drank alcohol only is 425 students.