To determine the probability that the second digit of a locker combination is 8, given that the first digit is already 8, let's follow these steps:
1. Understand the range of possible digits: Nonzero digits range from 1 to 9. Hence, each digit can be one of the nine numbers: 1, 2, 3, 4, 5, 6, 7, 8, or 9.
2. Determine the total number of possible outcomes: Since the second digit can also be any digit from 1 to 9, there are 9 possible choices for the second digit.
3. Identify the favorable outcome: We are interested in the specific event where the second digit is 8. There is only 1 favorable outcome (the digit being 8).
4. Calculate the probability: The probability is the number of favorable outcomes divided by the total number of possible outcomes.
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes (getting an 8)}}{\text{Total number of possible outcomes}}
\][/tex]
Plug in the numbers:
[tex]\[
\text{Probability} = \frac{1}{9}
\][/tex]
Therefore, the probability that the second number is 8, given that the first number is 8, is \(\frac{1}{9}\).
Thus, the correct answer is:
[tex]\[
\boxed{\frac{1}{9}}
\][/tex]
