4.3 .3 Quiz: Simulation and Modeling with Data Question 6 of 10 In a randomly generated list of numbers from 0 to 7 , what is the chance that each number will occur? A. \( \frac{1}{6} \) B. \( \frac{1}{9} \) C. \( \frac{1}{6} \) D. \( \frac{1}{5} \)

To determine the chance that each number will occur in a randomly generated list of numbers from 0 to 7, we first need to identify the total number of possible outcomes and the number of favorable outcomes. 1. **Identify the range of numbers**: The numbers range from 0 to 7, which gives us a total of 8 possible numbers (0, 1, 2, 3, 4, 5, 6, 7). 2. **Calculate the probability of each number occurring**: Since the numbers are generated randomly and uniformly, the probability of any specific number occurring is given by the formula: \[ P(\text{specific number}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \] In this case, the number of favorable outcomes for any specific number (e.g., 0) is 1, and the total number of outcomes is 8. Thus, the probability for each number is: \[ P = \frac{1}{8} \] Now, let's compare this with the provided options: A. \( \frac{1}{6} \) B. \( \frac{1}{9} \) C. \( \frac{1}{6} \) D. \( \frac{1}{5} \) None of the options match \( \frac{1}{8} \). Therefore, it seems there might be an error in the options provided, as the correct probability for each number occurring in a random list from 0 to 7 is \( \frac{1}{8} \). If you need to select the closest option, none of them are correct. However, if you are looking for the probability of a number occurring in a different context or with a different range, please clarify.