Probability And Odds
Probability and odds are two ways to express chance. In the vast majority of cases, there is no compelling reason to choose one over the other. Most scientists prefer to think about probabilities rather than odds, but this is a matter of habit and training rather than logic.
Probability and Odds Definition
The distinction is straightforward:
- The probability of an event occurring is the fraction of times you expect to see it in a large number of trials. The probabilities are always between 0 and 1.
- The odds are calculated by dividing the probability of an event occurring by the probability of it not occurring.
A probability of 0 is the same as odds of 0. Odds less than 1.0 are equal to probabilities between 0 and 0.5. The odds of 0.5 are the same as the odds of 1.0. Consider the following scenario: Flipping a coin to heads has a 50% chance of landing on heads. “Fifty: fifty,” which equals 1.0, are the odds.
The odds increase from 1.0 to infinity as the probability increases from 0.5 to 1.0. If the probability is 0.75, for example, the odds are 75:25, or three to one, or 3.0.
The probability is almost 1.00 when the odds are high (million to one). The probability is tiny, almost zero, if the odds are tiny (one in a million).
Converting odds and probability:
- To convert a probability to odds, divide it by one minus that probability. So, if the probability is 10%, or 0.10, the odds are 0.1/0.9, or “one to nine,” or 0.111.
- Divide the odds by one plus the odds to convert from odds to probability. To convert 1/9 odds to a probability, divide 1/9 by 10/9, which yields a probability of 0.10.
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