The number lock of a suitcase has 4 wheels with 10 digits, i.e. fro 0 to 9. The lock open with a sequence of 4 digits with repeats allowed. What is the probability of a person getting the right sequence to open the suit case?

Answer

To solve the problem, we need to determine the probability of a person successfully opening a suitcase lock that has a sequence of 4 digits, with each digit ranging from 0 to 9, and with repetitions allowed.

### Step-by-Step Solution:

1. **Identify the Total Number of Digits**:
The digits available are from 0 to 9, which gives us a total of 10 different digits.

2. **Determine the Length of the Sequence**:
The lock requires a sequence of 4 digits.

3. **Calculate the Total Number of Possible Sequences**:
Since each of the 4 positions in the sequence can be filled with any of the 10 digits, and repetitions are allowed, the total number of possible sequences can be calculated using the formula:
\[ \text{Total Sequences} = 10^4 \]
\[ \text{Total Sequences} = 10 \times 10 \times 10 \times 10 = 10,000 \]

4. **Identify the Number of Favorable Outcomes**:
There is only one specific sequence that will open the suitcase, which is the correct combination. Thus, the number of favorable outcomes is 1.

5. **Calculate the Probability**:
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} \]
Substituting the values we have:
\[ \text{Probability} = \frac{1}{10,000} \]

### Final Answer:
The probability of a person getting the right sequence to open the suitcase is:
\[ \frac{1}{10,000} \]