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, we can follow these steps:

### Step 1: Understand the given probability
The probability of the occurrence of an event is given as \( P(A) = \frac{3}{7} \).

### Step 2: Use the formula for non-occurrence
The probability of the non-occurrence of the event, denoted as \( P(A') \), can be calculated using the formula:
\[ P(A') = 1 - P(A) \]

### Step 3: Substitute the given probability
Now, we substitute the value of \( P(A) \) into the formula:
\[ P(A') = 1 - \frac{3}{7} \]

### Step 4: Calculate the non-occurrence probability
To perform the subtraction, we convert 1 into a fraction with a denominator of 7:
\[ 1 = \frac{7}{7} \]
Now we can subtract:
\[ P(A') = \frac{7}{7} - \frac{3}{7} = \frac{7 - 3}{7} = \frac{4}{7} \]

### Step 5: Conclusion
Thus, the probability of the non-occurrence of the event is:
\[ P(A') = \frac{4}{7} \]

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