The odds in favour of occurrence of an event are `2:5`. Find the probability of the occurrence of the event.

Explanation

To find the probability of the occurrence of an event given the odds in favor of the event are 2:5, we can follow these steps:

### Step 1: Understand the Odds
The odds in favor of an event are given as 2:5. This means that for every 2 favorable outcomes, there are 5 unfavorable outcomes.

### Step 2: Identify Favorable and Unfavorable Outcomes
From the odds:
- Favorable outcomes (occurrence of the event) = 2
- Unfavorable outcomes (non-occurrence of the event) = 5

### Step 3: Calculate Total Outcomes
To find the total number of outcomes, we add the favorable and unfavorable outcomes together:
\[ \text{Total outcomes} = \text{Favorable outcomes} + \text{Unfavorable outcomes} = 2 + 5 = 7 \]

### Step 4: Calculate the Probability
The probability of the occurrence of the event is given by the formula:
\[ \text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{2}{7} \]

### Final Answer
Thus, the probability of the occurrence of the event is:
\[ \frac{2}{7} \]

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