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The probability that the prisoner does not take classes

The table provided shows the distribution of inmates across different age groups and educational choices, with three categories: taking high school courses, taking college courses, or taking neither. To determine the probability that a prisoner does not take any classes (neither high school nor college), we need to consider the total number of inmates and how many of them fall under the "Neither" category.

Here’s the breakdown:

- **Under 30**:
  - High School: 52
  - College: 109
  - Neither: 460
- **30 and Over**:
  - High School: 21
  - College: 34
  - Neither: 360

**Step 1: Total number of inmates**
- Under 30: \( 52 + 109 + 460 = 621 \)
- 30 and Over: \( 21 + 34 + 360 = 415 \)
- Total inmates = \( 621 + 415 = 1036 \)

**Step 2: Number of inmates who take "Neither" (no classes)**
- Under 30: 460
- 30 and Over: 360
- Total in "Neither" = \( 460 + 360 = 820 \)

**Step 3: Probability that a prisoner does not take any classes**
This is calculated by dividing the number of inmates who take neither by the total number of inmates:

\[
P(\text{Neither}) = \frac{820}{1036} \approx 0.791
\]

Thus, the probability that a prisoner does not take any classes is approximately 0.791, or 79.1%.

Would you like more details or have any questions? 

Here are five related questions you could explore:
1. What is the probability that a prisoner under 30 takes any class (either high school or college)?
2. What percentage of prisoners over 30 take college courses?
3. How does the probability of taking high school courses compare between the two age groups?
4. What is the total percentage of prisoners participating in any form of education?
5. How would the probability change if more prisoners under 30 took high school courses?

**Tip:** Probabilities are always between 0 and 1, where 0 means impossible and 1 means certain.

Calculate the probability that a prisoner does not take any classes using survey data from federal prison inmates. Analyze the distribution of prisoners under 30 and over 30 across different educational choices. Learn key probability concepts suitable for Grades 6-8.

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