The odds in favour of occurrence of an event are 5:13. find the probability that it will occur.

Answer

To find the probability of an event occurring when the odds in favor of its occurrence are given as 5:13, we can follow these steps:

### Step-by-Step Solution:

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

2. **Identifying Favorable and Unfavorable Outcomes**:
- Favorable outcomes = 5
- Unfavorable outcomes = 13

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

4. **Calculating Probability**:
- The probability of an event occurring (P(E)) is given by the formula:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} \]
- Plugging in the values:
\[ P(E) = \frac{5}{18} \]

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