To determine the probability of being assigned the specific code "A123" from all possible 4-digit codes, we need to follow several steps, considering the constraints given.
### Step-by-Step Solution:
1. Understand the Structure of the Code:
- The code begins with 1 letter from the English alphabet.
- It then has 3 digits, each digit ranging from 0 to 9.
2. Calculate the Total Number of Possible Codes:
- There are 26 letters in the English alphabet.
- Each of the 3 digits can be any one of 10 digits (0 through 9).
To find the total number of possible combinations, we multiply the number of choices for each part of the code.
[tex]\[
\text{Total Possible Codes} = \text{Number of letters} \times (\text{Number of digits})^3
\][/tex]
Substituting the values:
[tex]\[
\text{Total Possible Codes} = 26 \times (10)^3
\][/tex]
Simplify to find the total combinations:
[tex]\[
\text{Total Possible Codes} = 26 \times 1000 = 26000
\][/tex]
3. Determine the Probability:
- The desired code "A123" is just one specific combination out of the total possible 26,000 combinations.
- The probability of getting this specific code is the number of favorable outcomes (1) divided by the total number of possible outcomes (26000).
[tex]\[
\text{Probability} = \frac{1}{\text{Total Possible Codes}} = \frac{1}{26000}
\][/tex]
4. Simplify the Probability:
- The fraction [tex]\(\frac{1}{26000}\)[/tex] is already in its simplest form.
So, the probability of being assigned the code "A123" is:
[tex]\[
\boxed{\frac{1}{26000}}
\][/tex]
