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

Given, probability

$=\frac{5}{14}$

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

$a=5$ 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 $9: 5$