The odds against of the occurrence of an event are `4:5` . 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 4:5, we can follow these steps:

### Step 1: Understand the Odds
The odds against the occurrence of an event are given as 4:5. This means:
- There are 4 unfavorable outcomes (the event does not occur).
- There are 5 favorable outcomes (the event occurs).

### Step 2: Calculate Total Outcomes
To find the total number of outcomes, we add the unfavorable and favorable outcomes together:
\[ \text{Total Outcomes} = \text{Unfavorable Outcomes} + \text{Favorable Outcomes} = 4 + 5 = 9 \]

### Step 3: Calculate the Probability
The probability of the occurrence of the event is given by the ratio of the number of favorable outcomes to the total number of outcomes:
\[ \text{Probability of Occurrence} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{5}{9} \]

### Conclusion
Thus, the probability of the occurrence of the event is:
\[ \frac{5}{9} \]

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