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If the odds against the occurrence of an event be 4 : 7, find the probability of the occurrence of the event.

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Best answer

We know that, 

If odds in favor of the occurrence an event are a:b, then the probability of an event to occur is \(\frac{a}{a+b}\), similarly, if odds are not in the favor of the occurrence an event are a:b, then the probability of not occurrence of the event is \(\frac{a}{a+b}\) 

We also know that,

Probability of occurring = 1 - the probability of not occurring

 =  \(1-\frac{a}{a+b}\) 

=  \(\frac{b}{a+b}\)  

Given a = 4 and b = 7 

Probability of occurrence = \(\frac{7}{4+7}\) = \(\frac{7}{11}\)

Conclusion: Probability that the event occurs is   \(\frac{7}{11}\)

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