If the odds in favour of an event are 4 to 5 , find the probability that it will occur .

Answer

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

### Step-by-Step Solution:

1. **Understanding Odds**: The odds in favor of an event are given as 4 to 5. This means that for every 4 favorable outcomes, there are 5 unfavorable outcomes.

2. **Identifying Favorable and Unfavorable Outcomes**:
- Favorable outcomes (the event occurring) = 4
- Unfavorable outcomes (the event not occurring) = 5

3. **Calculating Total Outcomes**:
- Total outcomes = Favorable outcomes + Unfavorable outcomes
- Total outcomes = 4 + 5 = 9

4. **Calculating Probability**:
- Probability (P) of the event occurring is given by the formula:
\[ P(A) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} \]
- Substituting the values we have:
\[ P(A) = \frac{4}{9} \]

5. **Final Answer**: The probability that the event will occur is \( \frac{4}{9} \).