To find out the chance that each number will occur in a randomly generated list of numbers ranging from 0 to 6, we need to understand the total number of distinct numbers possible in this range.
1. Identify the Range and Total Numbers:
- The numbers range from 0 to 6.
- This inclusive range means it includes 0, 1, 2, 3, 4, 5, and 6.
2. Count the Distinct Numbers:
- Total distinct numbers from 0 to 6 are: [tex]\( 0, 1, 2, 3, 4, 5, 6 \)[/tex].
- Counting these gives us a total of 7 distinct numbers.
3. Determine the Probability:
- Probability is the chance that a specific event will occur.
- Since each number is equally likely to occur and we're picking one number out of 7, the probability that each specific number will occur is:
[tex]\[
\text{Probability} = \frac{1}{\text{Total distinct numbers}}
\][/tex]
- Substituting the total distinct numbers (7) into the equation gives:
[tex]\[
\text{Probability} = \frac{1}{7}
\][/tex]
Since we have calculated the chance for each number to occur based on the total distinct numbers in the given range, the correct probability is:
[tex]\[
\boxed{\frac{1}{7}}
\][/tex]
