Using a computer program that can generate random
integers on the interval (0, 9) with equal probabilities,
generate 1,000 such integers and use the frequency interpretation to estimate the probability that such a randomly
chosen integer will have a value less than 1.


To estimate the probability that a randomly chosen integer from the interval \( (0, 9) \) will have a value less than 1 using a frequency interpretation, follow these steps:

### Steps:
1. **Generate 1,000 random integers**: The integers are randomly generated from the interval \( [0, 9] \) (inclusive) with equal probabilities.
   
2. **Count the occurrences of integers less than 1**: In this case, the only integer less than 1 in the interval \( [0, 9] \) is 0.

3. **Calculate the frequency**: The frequency of 0 appearing in the 1,000 generated integers will give an estimate of the probability.

4. **Estimate the probability**:
   \[
   P(\text{integer} < 1) = \frac{\text{count of integers less than 1}}{1000}
   \]

The **theoretical probability** of selecting an integer less than 1 is:
\[
P(\text{integer} < 1) = \frac{\text{number of integers less than 1}}{\text{total number of integers in the interval}} = \frac{1}{10} = 0.1
\]
You can compare the estimated probability from your experiment with this theoretical value.

Would you like help with generating the random integers or performing the frequency calculation? Feel free to upload your data or request specific assistance with the program.

### Questions to explore:
1. How does increasing the sample size affect the accuracy of the estimated probability?
2. What are some real-life applications of the frequency interpretation of probability?
3. What would the probability be if we expanded the range to \( (0, 99) \)?
4. How could you verify that your random number generator is truly generating integers with equal probability?
5. How does the concept of the Law of Large Numbers relate to this experiment?

**Tip**: Increasing the number of random trials will improve the accuracy of your estimated probability, approaching the true theoretical value.

Using a computer program that can generate random integers on the interval (0, 9) with equal probabilities, generate 1,000 such integers and use the frequency interpretation to estimate the probability that such a randomly chosen integer will have a value less than 1.

Learn how to estimate the probability that a randomly chosen integer from the interval (0, 9) will be less than 1 using a computer program. This guide covers random sampling, frequency interpretation, and comparison with theoretical probability, ideal for Grades 9-12.

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