The odds against of the occurrence of an event are `6:7`. Find the probability of the non-occurrence of the event.

Explanation

To solve the problem, we need to find the probability of the non-occurrence of an event given the odds against its occurrence.

### Step-by-Step Solution:

1. **Understanding Odds Against**:
The odds against the occurrence of an event are given as \(6:7\). This means that there are 6 unfavorable outcomes (the event does not occur) and 7 favorable outcomes (the event occurs).

2. **Total Outcomes**:
To find the total number of outcomes, we add the unfavorable and favorable outcomes together:
\[ \text{Total outcomes} = \text{Unfavorable outcomes} + \text{Favorable outcomes} = 6 + 7 = 13 \]

3. **Probability of Non-Occurrence**:
The probability of non-occurrence of the event can be calculated using the formula:
\[ P(\text{Non-occurrence}) = \frac{\text{Number of unfavorable outcomes}}{\text{Total outcomes}} \]
Substituting the values we have:
\[ P(\text{Non-occurrence}) = \frac{6}{13} \]

4. **Final Result**:
Therefore, the probability of the non-occurrence of the event is:
\[ \frac{6}{13} \]

### Summary:
The probability of the non-occurrence of the event is \( \frac{6}{13} \).

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