To find the probability of randomly selecting the correct access code on the first try, we need to determine how many possible codes can be formed and how many of those codes are correct.

Step 1: Total number of possible codes

Each digit of the access code can be any number from 1 to 9. Since the code has three digits, and each digit can be chosen independently, the total number of possible codes is calculated as:

$9 \times 9 \times 9 = 729$

Step 2: Number of correct codes

There is only one correct access code.

Step 3: Probability

The probability $P$ of selecting the correct code on the first try is given by the ratio of the number of correct codes to the total number of possible codes:

$P = \frac{1}{729}$

So, the probability of randomly selecting the correct access code on the first try is:

$\boxed{\frac{1}{729}}$

Would you like more details on probability, or do you have any other questions?

Here are five related questions to explore:

1. How does the probability change if the code has 4 digits?
2. What if the digits can be from 0 to 9 instead of 1 to 9?
3. How many different codes are there if no digit can be repeated?
4. What is the probability of guessing a two-digit access code correctly?
5. What is the probability of guessing a correct access code if one digit is given?

Tip: When calculating probabilities, always ensure that you correctly identify the total possible outcomes and the number of favorable outcomes.