The odds against of an event are 5:7 , find the probility of occurrence of this event .

Options

A. `3/8`
B. `7/12`
C. `2/7`
D. `5/12`

Answer

To find the probability of occurrence of an event when the odds against it are given as 5:7, we can follow these steps:

### Step 1: Understand the Odds
The odds against an event are given as 5:7. This means that for every 5 unfavorable outcomes, there are 7 favorable outcomes.

### Step 2: Define Unfavorable and Favorable Outcomes
From the odds:
- Unfavorable outcomes = 5 parts
- Favorable outcomes = 7 parts

### Step 3: Calculate Total Outcomes
To find the total number of outcomes, we add the unfavorable and favorable outcomes together:
\[ \text{Total outcomes} = \text{Unfavorable outcomes} + \text{Favorable outcomes} = 5 + 7 = 12 \]

### Step 4: Calculate the Probability of Occurrence
The probability of occurrence of the event is given by the formula:
\[ \text{Probability of occurrence} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} \]
Substituting the values we have:
\[ \text{Probability of occurrence} = \frac{7}{12} \]

### Final Answer
Thus, the probability of occurrence of the event is:
\[ \frac{7}{12} \]

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