Question

An anonymous survey of college students was taken to determine behaviors regarding alcohol, cigarettes, and illegal drugs. The results were as follows: 842 drankalcohol regularly, 665 smoked cigarettes, 207 used illegal drugs, 407 drank alcohol regularly and smoked cigarettes, 110 drank alcohol regularly and used illegal drugs,120 smoked cigarettes and used illegal drugs, 92 engaged in all three behaviors, and 131 engaged in none of these behaviors.Answer the following parts for the question: a, b, c, d, e, f, and g.A) how many students were surveyed?B) How many smoked cigarettes OR used illegal drugs?c) how many used illegal drugs only?d) how many smoked cigarettes AND used illegal drugs, BUT did not drink alcohol?e) how many drank alcohol OR used illegal drugs, BUT did not smoke cigarettes? f) how many engaged in exactly two of these behaviors? g) how many engaged in at least once of these behaviors?

Answer 1

Given:

Number of students who drank alcohol regularly = 842

Number of students who smoked cigarettes = 665

Number of students who used illegal drugs = 207

Number of students who drank and smoked = 407

Number of students who drank and used illegal drugs = 110

Number of students who smoked and used illegal drugs = 120

Number of students who did all three = 92

Number of students who did none = 131

• Let's find the number of students that were surveyed.

Here, we are to illustrate using a Venn Diagram.

We have:

We have the following:

• Number who drank and smoked only = 407 - 92 = 315

,

• Number who drank and used drugs only = 110 - 92 = 18

,

• Number who smoked and used drugs only = 120 - 92 = 28

• Number of students who drank alcohol only = 842 - 315 - 18 - 92 = 417

,

• Number of students who smoked only = 665 - 315 - 28 - 92 = 230

,

• Number of students who used drugs only = 207 - 18 - 28 - 92 = 69

The figures are shown in the Venn diagram.

Therefore, the total number of students surveyed will be the sum of all values in the Venn diagram.

T = 417 + 28 + 230 + 315 + 69 + 18 + 131 + 92 = 1300

Therefore, the total number of students surveyed is 1300 students.

• Part B.

The number of students who smoked or used illegal drug will be:

230 + 69 + 18 + 28 + 92 + 315 = 752

Therefore, 752 students smoked or used illegal drugs.

Part C.

c) how many used illegal drugs only?

According to the Venn diagram only 69 students used illegal drugs only.

Part D.

d) how many smoked cigarettes AND used illegal drugs, BUT did not drink alcohol?

According to the Venn diagram, the number is 28 .

Part E.

e) how many drank alcohol OR used illegal drugs, BUT did not smoke cigarettes?

Number of students who drank alcohol or used illegal drugs but did not smoke will be:

417 + 69 + 18 = 504

Part F.

f) how many engaged in exactly two of these behaviors?

315 + 18 + 28 = 361

Therefore, 361 students engaged in exactly two of these behaviors.

Part G.

How many engaged in at least once of these behaviors?

1300 - 131 = 1169

Therefore 1169 students engaged in at least one of these behaviors

ANSWER:

• A) 1300

,

• B) 752

,

• C). 69

,

• D). 28

,

• E.) 504

,

• F). 361

,

• G). 1169