If the odds in favour of an eventare 2:1 then the probability of its occurrence is

Options

A. `2/3`
B. `1/3`
C. `1/2`
D. `1/3`

Answer

To find the probability of an event when the odds in favor of the event are given as 2:1, we can follow these steps:

### Step 1: Understand the Odds
The odds in favor of an event being 2:1 means that for every 2 favorable outcomes, there is 1 unfavorable outcome.

### Step 2: Identify Favorable and Unfavorable Outcomes
From the odds of 2:1, we can identify:
- Favorable outcomes (A) = 2
- Unfavorable outcomes (not A) = 1

### Step 3: Calculate Total Outcomes
Total outcomes can be calculated by adding the favorable and unfavorable outcomes:
\[ \text{Total Outcomes} = \text{Favorable Outcomes} + \text{Unfavorable Outcomes} = 2 + 1 = 3 \]

### Step 4: Calculate Probability
The probability of the event occurring (P(A)) is given by the formula:
\[ P(A) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} = \frac{2}{3} \]

### Conclusion
Thus, the probability of the occurrence of the event is:
\[ \boxed{\frac{2}{3}} \]

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