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Odds = & Event occurring/Total outcomes : Event not occurring/Total outcomes & _(P( A)) _(P( A'))
When an event does not occur, that is called the complement of the event. Since the denominators of both probabilities are the same, the odds of an event can also be understood as the ratio of favorable outcomes to unfavorable outcomes.
Odds = Favorable outcomes/Unfavorable outcomes
Suppose a six-sided die is rolled and either a 5 or 6 is needed to win the game.
| Outcomes | Odds of the Event | |
|---|---|---|
| Favorable | 5, 6_2 | 2/4 = 1/2 |
| Unfavorable | 1, 2, 3, 4_4 |
The odds of rolling either a 5 or 6 on a six-sided die are 1 to 2. This ratio may also be written as 1:2.