https://file.aiquickdraw.com/mathbot/file/1726376954941i0z3ykg0.jpg

Let's break down the problem and extract the relevant information from the image you provided:

### Given dataLet's break down the problem and extract the relevant information from the image you provided:

### Given 
- **853** students drank alcohol regularly.
- **648** students smoked cigarettes.
- **192** students used illegal drugs.
- **399** students drank alcohol regularly and smoked cigarettes.
- **105** students drank alcohol regularly and used illegal drugs.
- **107** students smoked cigarettes and used illegal drugs.
- **82** students engaged in all three behaviors (drank alcohol, smoked cigarettes, and used illegal drugs).
- **336** students engaged in none of these behaviors.

### Questions:
1. **(a)** How many students were surveyed?
2. **(b)** How many smoked cigarettes or used illegal drugs?
3. **(c)** How many smoked cigarettes only?
4. **(d)** How many drank alcohol and used illegal drugs, but did not smoke cigarettes?
5. **(e)** How many smoked cigarettes or used illegal drugs, but did not drink alcohol?
6. **(f)** How many engaged in exactly two of these behaviors?
7. **(g)** How many engaged in at least one of these behaviors?

---

I'll start by solving the first part of the problem (a) and use this data to solve the subsequent questions.

### Part (a): 
The total number of students surveyed can be found by adding the number of students who engaged in any behavior and those who engaged in none. That is:

\[
\text{Total surveyed} = (\text{Students engaging in behaviors}) + (\text{Students engaging in none})
\]

I'll calculate that now.### (a) How many students were surveyed?

The total number of students surveyed is **1,189**.

Now, let's proceed to the other questions using the provided data### (a) How many students were surveyed?

The total number of students surveyed is **1,189**.

Now, let's proceed to the other questions using the provided 

---

### Part (b): 
**How many smoked cigarettes or used illegal drugs?**

This question asks for students who either smoked cigarettes, used illegal drugs, or did both. To compute this, we need to use the principle of inclusion and exclusion:

\[
\text{Smoked or used drugs} = (\text{Smoked cigarettes}) + (\text{Used illegal drugs}) - (\text{Smoked and used drugs})
\]

I'll calculate this next.It seems like I can't do more advanced data analysis right now. Please try again later. However, if you'd like, I can guide you through solving the rest of the problem manually.

Would you like to proceed that way, or perhaps try re-uploading? Feel free to ask any questions!

An anonymous survey of college students was taken to determine behaviors regarding alcohol, cigarettes, and illegal drugs. The results were as follows: 853 drank alcohol regularly, 648 smoked cigarettes, 192 used illegal drugs, 399 drank alcohol regularly and smoked cigarettes, 105 drank alcohol regularly and used illegal drugs, 107 smoked cigarettes and used illegal drugs, 82 engaged in all three behaviors, and 336 engaged in none of these behaviors. Answer the following questions: a) How many students were surveyed? b) How many smoked cigarettes or used illegal drugs? c) How many smoked cigarettes only? d) How many drank alcohol and used illegal drugs, but did not smoke cigarettes? e) How many smoked cigarettes or used illegal drugs, but did not drink alcohol? f) How many engaged in exactly two of these behaviors? g) How many engaged in at least one of these behaviors?

Analyze data from a college student survey about behaviors related to alcohol, cigarettes, and illegal drugs. Learn how to use set theory and the inclusion-exclusion principle to answer various questions such as: How many students engaged in these behaviors? How many engaged in exactly two of them? Suitable for Grades 10-12.

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