The odds in favour if an event are 2 :7 find the probability of occurrence of this event .

Options

A. `2/9`
B. `5/12`
C. `7/12`
D. `2/5`

Answer

To find the probability of occurrence of an event given the odds in favor are 2:7, we can follow these steps:

### Step-by-step Solution:

1. **Understand the Odds**: The odds in favor of an event are given as 2:7. This means that for every 2 favorable outcomes, there are 7 unfavorable outcomes.

2. **Define Favorable and Unfavorable Outcomes**:
- Favorable outcomes (successes) = 2
- Unfavorable outcomes (failures) = 7

3. **Calculate Total Outcomes**:
- Total outcomes = Favorable outcomes + Unfavorable outcomes
- Total outcomes = 2 + 7 = 9

4. **Use the Probability Formula**:
- The probability of an event is given by the formula:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
- Here, \( P(E) = \frac{2}{9} \)

5. **Final Answer**:
- The probability of occurrence of the event is \( \frac{2}{9} \).

### Summary:
The probability of occurrence of the event given the odds in favor of 2:7 is \( \frac{2}{9} \).

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