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 when the odds against it are given as 3:4, we can follow these steps:

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

### Step 2: Identify the number of favorable and unfavorable outcomes
From the odds 3:4:
- Unfavorable outcomes = 3
- Favorable outcomes = 4

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

### Step 4: Calculate the probability of the event occurring
The probability of an event occurring is given by the ratio of the number of favorable outcomes to the total number of 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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