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