The probability of the occurrence of an event is `3/7`
The probability of non-occurrence of the event is:

Options

A. `3/7`
B. `4/7`
C. `2/7`
D. None of these

Explanation

To solve the problem, we need to find the probability of the non-occurrence of an event given that the probability of the occurrence of that event is \( \frac{3}{7} \).

### Step-by-Step Solution:

1. **Understand the relationship between occurrence and non-occurrence:**
The probability of an event occurring and the probability of it not occurring must sum up to 1. This can be expressed mathematically as:
\[ P(\text{occurrence}) + P(\text{non-occurrence}) = 1 \]

2. **Identify the given probability:**
We are given that the probability of the occurrence of the event is:
\[ P(\text{occurrence}) = \frac{3}{7} \]

3. **Set up the equation to find the non-occurrence probability:**
Let \( P(\text{non-occurrence}) \) be the probability of the non-occurrence of the event. According to the relationship mentioned in step 1, we can express it as:
\[ P(\text{non-occurrence}) = 1 - P(\text{occurrence}) \]

4. **Substitute the known value into the equation:**
Now, substitute \( P(\text{occurrence}) \) with \( \frac{3}{7} \):
\[ P(\text{non-occurrence}) = 1 - \frac{3}{7} \]

5. **Perform the subtraction:**
To subtract \( \frac{3}{7} \) from 1, we can express 1 as \( \frac{7}{7} \):
\[ P(\text{non-occurrence}) = \frac{7}{7} - \frac{3}{7} = \frac{7 - 3}{7} = \frac{4}{7} \]

6. **Conclusion:**
Therefore, the probability of the non-occurrence of the event is:
\[ P(\text{non-occurrence}) = \frac{4}{7} \]

### Final Answer:
The probability of non-occurrence of the event is \( \frac{4}{7} \).