# Probability vs. odds

FAQ# 1466    Last Modified 23-March-2009

Chance can be expressed either as a probability or as odds. In most contexts, there is no particular reason to prefer one over the other. Most scientists tend to feel more comfortable thinking about probabilities than odds, but that is a matter of training and custom, not logic.

The distinction is simple:

• The probability that an event will occur is the fraction of times you expect to see that event in many trials. Probabilities always range between 0 and 1.
• The odds are defined as the probability that the event will occur divided by the probability that the event will not occur.

A probability of 0 is the same as odds of 0. Probabilities between 0 and 0.5 equal odds less than 1.0. A probability of 0.5 is the same as odds of 1.0. Think of it this way: The probability of flipping a coin to heads is 50%. The odds are “fifty: fifty,” which equals 1.0.

As the probability goes up from 0.5 to 1.0, the odds increase from 1.0 to approach infinity. For example, if the probability is 0.75, then the odds are 75:25, three to one, or 3.0.

If the odds are high (million to one), the probability is almost 1.00. If the odds are tiny (one to a million), the probablility is tiny, almost zero.

Converting between odds and probability is straightforward:

• To convert from a probability to odds, divide the probability by one minus that probability. So if the probability is 10% or 0.10 , then the odds are 0.1/0.9 or ‘1 to 9’ or 0.111.
• To convert from odds to a probability, divide the odds by one plus the odds. So to convert odds of 1/9 to a probability, divide 1/9 by 10/9 to obtain the probability of 0.10.

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