The odds against of an event are `3:4`. Find the probability of the occurrence of the event.

Explanation

To find the probability of the occurrence of an event given the odds against it are `3:4`, we can follow these steps:

### Step 1: Understand the Odds Against
The odds against an event are given as `3:4`. This means that for every 3 unfavorable outcomes, there are 4 favorable outcomes.

### Step 2: Identify Favorable and Unfavorable Outcomes
From the odds `3:4`:
- Unfavorable outcomes (against the event) = 3
- Favorable outcomes (for the event) = 4

### Step 3: Calculate Total Outcomes
To find the total number of outcomes, we add the favorable and unfavorable outcomes together:
\[ \text{Total Outcomes} = \text{Favorable Outcomes} + \text{Unfavorable Outcomes} = 4 + 3 = 7 \]

### Step 4: Calculate the Probability of Occurrence
The probability of the occurrence of the event is given by the ratio of favorable outcomes to total outcomes:
\[ \text{Probability of Occurrence} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{4}{7} \]

### Final Answer
Thus, the probability of the occurrence of the event is:
\[ \frac{4}{7} \]

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