The odds against of an event `5:3`. 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 5:3, we can follow these steps:

### Step 1: Understand the Odds
The odds against an event are given as 5:3. This means that for every 5 unfavorable outcomes, there are 3 favorable outcomes.

### Step 2: Identify Favorable and Unfavorable Outcomes
From the odds:
- Unfavorable outcomes = 5
- Favorable outcomes = 3

### Step 3: Calculate Total Outcomes
To find the total number of outcomes, we add the favorable and unfavorable outcomes together:
\[ \text{Total Outcomes} = \text{Favorable Outcomes} + \text{Unfavorable Outcomes} = 3 + 5 = 8 \]

### Step 4: Calculate the Probability
The probability of the occurrence of the event is given by the formula:
\[ \text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} \]
Substituting the values we have:
\[ \text{Probability} = \frac{3}{8} \]

### Step 5: Conclusion
Thus, the probability of the occurrence of the event is:
\[ \frac{3}{8} \]

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