If 5/14 Is the probability of occurrence of an event, find

Question:

If 5/14 Is the probability of occurrence of an event, find

(i) the odds in favor of its occurrence

(ii) the odds against its occurrence

 

Solution:

(i) We know that,

If odds in favor of the occurrence an event are a:b, then the probability of an event to

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

Given, probability $=\frac{5}{14}$

We know, probability $=\frac{a}{a+b} .$ So, $\frac{a}{a+b}=\frac{5}{14}$

a = 5 and a+b = 14 i.e. b = 9

odds in favor of its occurrence = a:b

= 5:9

Conclusion: Odds in favor of its occurrence is 5:9

(ii) As we solved in part (i), $a=5$ and $b=9$

As we know, odds against its occurrence is b:a

=9: 5

Conclusion: Odds against its occurrence is 9:5

 

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