Question:
The odds in favor of the occurrence of an event are 8 : 13. Find the probability that the event will occur.
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 $\frac{a}{a+b}$ which indirectly came from
Probability of the occurrence of an event
$=\frac{\text { Total no.of Desired outcomes }}{\text { Total no.of outcomes }}$
Where, Total no.of desired outcomes = a, and total no.of outcomes = a+b
Given a = 8, b= 13
The probability that the event occurs
$=\frac{8}{8+13}$
$=\frac{8}{21}$
Conclusion: Probability that the event occurs is $\frac{8}{21}$