**Prison Education In a federal prison, inmates can select to complete high school, take college courses, or do neither. The following survey results were obtained using ages of the inmates.**


**Age**

**High School Courses**

**College Courses**


**Neither**

**Under** 

**30**

**54**

**106**

**449**

**30**

 **and Over**

**28**

**32**

**363**

**Choose a prisoner at random. Find the following probabilities. Round the answers to at least three decimal places.**

The probability that the prisoner is under 

30

 and is taking either a high school class or a college class is



We are asked to find the probability that a randomly selected prisoner is **under 30** and is taking either a **high school class** or a **college class**. 

Let's break down the information given:

### Age Categories:
- **Under 30**:
  - High School Courses: 54 inmates
  - College Courses: 106 inmates
  - Neither: 449 inmates

- **30 and Over**:
  - High School Courses: 28 inmates
  - College Courses: 32 inmates
  - Neither: 363 inmates

### Step 1: Total number of prisoners
First, we need the total number of prisoners in the survey:
\[
\text{Total prisoners} = (54 + 106 + 449) + (28 + 32 + 363) = 609 + 423 = 1032
\]

### Step 2: Prisoners under 30 taking a high school or college course
The question asks for the probability that the prisoner is under 30 and taking either a high school or college class. We will add the number of prisoners under 30 taking either of these courses:

\[
\text{Prisoners under 30 taking either high school or college course} = 54 + 106 = 160
\]

### Step 3: Calculate the probability
The probability \( P \) is calculated by dividing the number of prisoners under 30 taking either high school or college classes by the total number of prisoners:

\[
P = \frac{\text{Prisoners under 30 taking high school or college course}}{\text{Total prisoners}} = \frac{160}{1032}
\]

\[
P = 0.155
\]

### Final Answer:
The probability that the prisoner is under 30 and is taking either a high school class or a college class is approximately **0.155** or **15.5%**.

Would you like to dive deeper into any of the steps or clarify the concepts?

### Further questions:
1. What is the probability that a prisoner is under 30 and not taking any courses?
2. What is the probability that a prisoner is over 30 and taking a college course?
3. What is the total percentage of prisoners under 30 in the survey?
4. How do you calculate conditional probabilities based on these results?
5. Can we apply the same steps to find probabilities of prisoners who are taking no classes at all?

**Tip**: Always ensure to add mutually exclusive events when combining probabilities, such as "high school" and "college" categories in this case.

Prison Education In a federal prison, inmates can select to complete high school, take college courses, or do neither. The following survey results were obtained using ages of the inmates. Age: High School Courses, College Courses, Neither. Under 30: 54, 106, 449. 30 and Over: 28, 32, 363. Choose a prisoner at random. Find the following probabilities. Round the answers to at least three decimal places. The probability that the prisoner is under 30 and is taking either a high school class or a college class is:

Discover how to calculate the probability that a prisoner under 30 in a federal prison is enrolled in high school or college courses. The problem uses basic statistics concepts, including probability calculations and data analysis, with a detailed solution. Suitable for high school students in Grades 9-12.

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