If 5/14 Is the probability of occurrence of an event, find (i) the od

1.	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
Answer» (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 = \(\frac{a}{a+b}\) 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

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

Answer»

(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 = \(\frac{a}{a+b}\)

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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