If the odds against the occurrence of an event be

Question:

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

Solution:

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 $\frac{\mathrm{a}}{\mathrm{a}+\mathrm{b}}$

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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