The probability of the occurrence of an event is `3/7`. Find the probability of the non occurrence of the event.

Explanation

To find the probability of the non-occurrence of an event given that the probability of its occurrence is \( \frac{3}{7} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the given information**:
We know that the probability of the occurrence of an event \( P(A) \) is given as \( \frac{3}{7} \).

2. **Recall the total probability rule**:
The sum of the probabilities of an event occurring and not occurring is always equal to 1. This can be expressed as:
\[ P(A) + P(A') = 1 \]
where \( P(A') \) is the probability of the non-occurrence of the event.

3. **Substitute the known value**:
We can substitute the known probability of occurrence into the equation:
\[ \frac{3}{7} + P(A') = 1 \]

4. **Solve for the probability of non-occurrence**:
To find \( P(A') \), we rearrange the equation:
\[ P(A') = 1 - \frac{3}{7} \]

5. **Calculate the right-hand side**:
To perform the subtraction, we need to express 1 in terms of a fraction with a denominator of 7:
\[ 1 = \frac{7}{7} \]
Now, we can subtract:
\[ P(A') = \frac{7}{7} - \frac{3}{7} = \frac{4}{7} \]

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

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

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