A locker can be opened by dialing a fixed three digit code from 000 to 999. A stranger who does not know the code, tries to open the locker by dialing three digits at random. Probability, that he opens the locker in first trail, is

Options

A. `1/1000`
B. `9/1000`
C. `99/100`
D. `99/1000`

Answer

To solve the problem, we need to determine the probability that a stranger can open a locker by dialing a three-digit code at random. The code can range from 000 to 999.

### Step-by-Step Solution:

1. **Determine the Total Number of Possible Codes:**
The codes range from 000 to 999. This gives us a total of:
\[ 999 - 000 + 1 = 1000 \text{ possible codes} \]

2. **Identify the Number of Successful Outcomes:**
Since there is only one correct code that will open the locker, the number of successful outcomes is:
\[ 1 \text{ (the correct code)} \]

3. **Calculate the Probability:**
The probability \( P \) of the stranger opening the locker on the first try is given by the formula:
\[ P(\text{opening the locker}) = \frac{\text{Number of successful outcomes}}{\text{Total number of possible outcomes}} \]
Substituting the values we found:
\[ P = \frac{1}{1000} \]

### Final Answer:
The probability that the stranger opens the locker on the first trial is:
\[ \frac{1}{1000} \]