To determine the probability that the third digit in the locker combination is 3, let's analyze the situation step by step.
1. Identify the available digits: The combination already uses the digits 1 and 2, so they can't be used for the third position. The available digits for the third position are: 3, 4, 5, 6, 7, 8, and 9.
2. Count the remaining digits: There are 7 possible digits remaining (3 through 9).
3. Determine the number of favorable outcomes: We're interested in the specific case where the third digit is 3. Hence, there is only 1 favorable outcome (where the third digit is 3).
4. Calculate the probability: The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Therefore, the probability is:
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
= \frac{1}{7}
\][/tex]
Thus, the probability that the third digit is 3 is \( \frac{1}{7} \).
So the correct answer is:
D) [tex]\( \frac{1}{7} \)[/tex]
