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To solve the problem of finding the probability that a randomly selected patient is a nonalcoholic with a nonelevated cholesterol level, let's first gather and organize the data provided:

- Total number of patients: 400
- Number of alcoholic patients: 80
  - Number of alcoholic patients with elevated cholesterol levels: 61
  - Number of alcoholic patients with nonelevated cholesterol levels: \(80 - 61 = 19\)
- Number of nonalcoholic patients: 320
  - Number of nonalcoholic patients with elevated cholesterol levels: 74
  - Number of nonalcoholic patients with nonelevated cholesterol levels: \(320 - 74 = 246\)

We need to find the probability that a randomly selected patient is a nonalcoholic with a nonelevated cholesterol level. The probability is given by the ratio of the number of nonalcoholic patients with nonelevated cholesterol levels to the total number of patients.

\[ P(\text{nonalcoholic with nonelevated cholesterol level}) = \frac{\text{Number of nonalcoholic patients with nonelevated cholesterol levels}}{\text{Total number of patients}} \]

Substituting the numbers:

\[ P(\text{nonalcoholic with nonelevated cholesterol level}) = \frac{246}{400} \]

Now, let's calculate this probability:

\[ P(\text{nonalcoholic with nonelevated cholesterol level}) = \frac{246}{400} = 0.615 \]

So, the probability is \( 0.615 \).

Do you want details or have any questions? Here are five questions you might want to ask:

1. How do we calculate the probability for the other parts of the problem?
2. What is the process for determining probabilities in similar scenarios?
3. Can you explain how to organize the data for probability calculations?
4. How would the probabilities change if the total number of patients were different?
5. Can you show how to solve for combined probabilities using this data?

**Tip:** Always double-check the complement values (e.g., nonelevated cholesterol level) to ensure the total counts are consistent with the given data.

Learn how to calculate the probability that a randomly selected patient is a nonalcoholic with a nonelevated cholesterol level. This example involves basic data analysis and probability concepts. Suitable for students in Grades 7-9.

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