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The odds in favor of the occurrence of an event are 8 : 13.

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 $\frac{8}{21}$