Odds in favour of occurrences of an event are 5:13, the probability that it will occur is..

Answer

To find the probability of an event given the odds in favor of its occurrence, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Odds**: The odds in favor of an event occurring are given as 5:13. This means that for every 5 favorable outcomes, there are 13 unfavorable outcomes.

2. **Identify Favorable and Unfavorable Outcomes**:
- Favorable outcomes (E) = 5
- Unfavorable outcomes (not E) = 13

3. **Calculate Total Outcomes**:
- Total outcomes = Favorable outcomes + Unfavorable outcomes
- Total outcomes = 5 + 13 = 18

4. **Calculate Probability**:
- The probability of the event occurring (P(E)) is given by the formula:
\[ P(E) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} \]
- Substituting the values:
\[ P(E) = \frac{5}{18} \]

5. **Final Answer**: The probability that the event will occur is \( \frac{5}{18} \).