The odds in favour of an event are 3 : 4. Find the probability of :
(i) Occurrence (ii) Non-occurrence of the event.

Answer

To solve the problem, we need to understand the relationship between odds and probability. The odds in favor of an event are given as 3:4. This means that for every 3 occurrences of the event, there are 4 non-occurrences.

### Step-by-Step Solution:

1. **Understanding Odds**:
- The odds in favor of an event being 3:4 means that there are 3 favorable outcomes (occurrences of the event) and 4 unfavorable outcomes (non-occurrences of the event).

2. **Total Outcomes**:
- To find the total number of outcomes, we add the favorable and unfavorable outcomes together:
\[ \text{Total Outcomes} = \text{Favorable Outcomes} + \text{Unfavorable Outcomes} = 3 + 4 = 7 \]

3. **Calculating Probability of Occurrence**:
- The probability of occurrence of the event can be calculated using the formula:
\[ P(\text{Occurrence}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} = \frac{3}{7} \]

4. **Calculating Probability of Non-Occurrence**:
- The probability of non-occurrence of the event can be calculated similarly:
\[ P(\text{Non-Occurrence}) = \frac{\text{Number of Unfavorable Outcomes}}{\text{Total Outcomes}} = \frac{4}{7} \]

### Final Answers:
- (i) Probability of occurrence: \( \frac{3}{7} \)
- (ii) Probability of non-occurrence: \( \frac{4}{7} \)