Odds of an event
If there are p outcomes favourable to a certain event and q outcomes unfavourable to the event in a sample space
then, odds in favour of the event = \(\frac{Number\,of\,favourable\,outcomes}{Number\,of\,unfavourable\,outcomes}\) = \(\frac{p}{q}\)
Odds against the event = \(\frac{Number\,of\,unfavourable\,outcomes}{Number\,of\,favourable\,outcomes}\) = \(\frac{q}{p}\)
If odds in favour of an event A are m : n , then
Probability of happening of event A= P(A) = \(\frac{m}{m+n}\)
Probability of not happening of event A = P(\(\bar A\)) = \(\frac{n}{m+n}\)