If the odds in favour of an event are 4:5, then the probability of non-occurrence of that event is

Options

A. `1/3`
B. `2/3`
C. `5/9`
D. `4/9`

Answer

To find the probability of non-occurrence of an event when the odds in favor of the event are given as 4:5, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Odds**: The odds in favor of an event being 4:5 means that for every 4 occurrences of the event, there are 5 non-occurrences.

2. **Identify Occurrences and Non-Occurrences**:
- Let the number of occurrences of the event be \(4\).
- Let the number of non-occurrences of the event be \(5\).

3. **Calculate Total Outcomes**:
- Total outcomes = Number of occurrences + Number of non-occurrences
- Total outcomes = \(4 + 5 = 9\).

4. **Calculate Probability of Non-Occurrence**:
- Probability of non-occurrence of the event = (Number of non-occurrences) / (Total outcomes)
- Probability of non-occurrence = \(5 / 9\).

5. **Conclusion**:
- The probability of non-occurrence of the event is \( \frac{5}{9} \).

### Final Answer:
The probability of non-occurrence of the event is \( \frac{5}{9} \).

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