To solve the problem of determining the number of possible three-digit pin codes and the probability of guessing the correct one on the first try, given an 8-key keypad with repetition allowed, we proceed as follows:

1. Calculate the Number of Possible Codes:

   Since the thief can choose any of the 8 digits (0-7) for each of the three positions in the pin code, the number of possible codes is calculated by: $8 \times 8 \times 8 = 8^3$

   Simplifying this: $8^3 = 512$

   So, the number of possible codes is 512.

2. Determine the Probability of a Correct Guess:

   The probability of guessing the correct code on the first try is the reciprocal of the number of possible codes since each code is equally likely: $\text{Probability} = \frac{1}{512}$

Therefore, the answers are:

• The number of possible codes is 512.
• The probability of a correct guess on the first try is $\frac{1}{512}$.

Would you like further details or have any questions? Here are some more questions you might find interesting:

1. What is the probability of guessing a four-digit pin code on the first try using a 10-key keypad?
2. How many possible combinations are there for a five-character password using lowercase letters?
3. What is the probability of guessing a 6-character alphanumeric password on the first try?
4. If repetition is not allowed, how many different three-digit codes can be formed from an 8-key keypad?
5. What is the probability of guessing a two-digit pin code with a 5-key keypad?

Tip: Understanding basic principles of probability and combinatorics can significantly help in solving similar problems effectively.