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If the odds against an event be 2 : 3, t...

If the odds against an event be 2 : 3, then the probability of its occurrence is

A

`(1)/(5)`

B

`(2)/(5)`

C

`(3)/(5)`

D

`(1)/(6)`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the probability of the occurrence of an event given the odds against it. The odds against an event being 2:3 means that for every 2 unfavorable outcomes, there are 3 favorable outcomes. ### Step-by-Step Solution: 1. **Understanding Odds Against**: - The odds against an event are given as 2:3. This means there are 2 unfavorable outcomes for every 3 favorable outcomes. 2. **Identifying Favorable and Unfavorable Outcomes**: - Unfavorable outcomes = 2 - Favorable outcomes = 3 3. **Calculating Total Outcomes**: - Total outcomes = Unfavorable outcomes + Favorable outcomes - Total outcomes = 2 + 3 = 5 4. **Calculating Probability of Occurrence**: - Probability of occurrence = (Number of favorable outcomes) / (Total outcomes) - Probability of occurrence = 3 / 5 5. **Final Answer**: - The probability of the occurrence of the event is **3/5**.
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