The odds against the occurrence of an event are 5 : 4. The probability of its occurrence is-

Options

A. `4/5`
B. `4/9`
C. `1/5`
D. `1/4`

Answer

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

### Step-by-Step Solution:

1. **Understand the Odds Against the Event**:
The odds against the occurrence of an event are given as 5:4. This means that for every 5 times the event does not occur, it occurs 4 times.

2. **Identify the Number of Occurrences and Non-Occurrences**:
From the odds 5:4, we can denote:
- Non-occurrences = 5
- Occurrences = 4

3. **Calculate Total Outcomes**:
The total outcomes can be calculated by adding the occurrences and non-occurrences together:
\[ \text{Total Outcomes} = \text{Occurrences} + \text{Non-Occurrences} = 4 + 5 = 9 \]

4. **Calculate the Probability of Occurrence**:
The probability of the occurrence of the event can be calculated using the formula:
\[ P(\text{Occurrence}) = \frac{\text{Number of Occurrences}}{\text{Total Outcomes}} = \frac{4}{9} \]

5. **Final Answer**:
Thus, the probability of the occurrence of the event is:
\[ \frac{4}{9} \]