Suppose the probability of an event is $$ \frac{26}{45} $$. What are the odds for the event happening? What are the odds against the event happening?

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1. Given the probability of the event is  
   $$
   p = \frac{26}{45}.
   $$
2. The probability of the event not happening is  
   $$
   1 - p = 1 - \frac{26}{45} = \frac{45}{45} - \frac{26}{45} = \frac{19}{45}.
   $$
3. The odds for the event happening are expressed as the ratio  
   $$
   \frac{p}{1-p} = \frac{\frac{26}{45}}{\frac{19}{45}} = \frac{26}{19}.
   $$  
   So, the odds for the event happening are $$26:19$$.

4. The odds against the event happening are the inverse ratio,  
   $$
   19:26.
   $$
The odds for the event happening are 26:19, and the odds against the event happening are 19:26.

Suppose the probability of an event is .
What are the odds for the event happening?
What are the odds against the event happening?

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