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A 3-digit code typically consists of digits ranging from 0 to 9. This means there are 10 possible digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) for each of the three positions in the code.
To calculate the total number of possible combinations, you can use the formula for combinations of independent events. Since each digit can be any of the 10 digits, the total number of combinations is:
\[ 10 \times 10 \times 10 = 10^3 = 1000 \]
Therefore, there are 1,000 possible combinations for a 3-digit code.
The chance of guessing the correct 3-digit code on your first attempt can be calculated using the total number of possible combinations. As established earlier, there are 1,000 possible combinations for a 3-digit code.
Since there is only 1 correct combination, the probability \( P \) of guessing the correct combination on your first attempt is given by:
\[ P(\text{correct guess}) = \frac{\text{Number of successful outcomes}}{\text{Total number of outcomes}} = \frac{1}{1000} \]
This can also be expressed as a decimal or percentage:
\[ P(\text{correct guess}) = 0.001 \quad \text{or} \quad 0.1% \]
So, the chance that you can guess the correct 3-digit code on your first attempt is 0.1%.
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