Odds express an event through successes relative to failures, while probability expresses successes relative to all possible outcomes. They are related but not interchangeable. section 2.1.2
Use these equivalent forms to move between probability and odds:
- Odds = successful outcomes / failed outcomes. section 2.1.2
- Odds = probability of success / probability of failure, where the two probabilities sum to 1. section 2.1.2
- Probability can be recovered from odds by dividing the odds by one plus the odds. section 2.1.2
- For a six-sided die, rolling a 4 has probability 1/6 and odds 1/5, or 0.2. section 3.2
Two-dice outcome
The probability that one die shows 1, 2, or 3 and the other shows 4, 5, or 6 is 9/36, or 25%. Its failure probability is 75%, so the odds are 0.25/0.75, or 0.33. section 3.2.3
>>> probability_double_sixes = 1 / 36
>>> probability_double_sixes_percent = probability_double_sixes * 100
>>> print(f'The probability of success equals: '
>>> f'{probability_double_sixes_percent}%')
The probability of success equals: 2.7777777777777777%
>>> probability_face_card = 12 / 52
>>> probability_face_card_percent = probability_face_card * 100
>>> print(f'The probability of success equals: '
>>> f'{probability_face_card_percent}%')
The probability of success equals: 23.076923076923077%
Compare probability calculations for a coin flip, double sixes, and a face card before converting selected results into odds. section 2.1.2
