Statistics Definitions > Chance vs Probability vs Odds

Probability is the study of the chance something will happen. The two terms—chance and probability—are often used as synonyms. If you’re talking about the **chance **something will happen, then that is **an informal way of saying probability.** For example, you might say you have a 10% chance of winning a raffle or you could also say there is a 10% probability you’ll win; they both mean the same thing.

Many other terms are used in the same way: when we say that an event is “likely”, “unlikely”, or “almost definitively” to happen, we are also talking about probability.

## Chance vs Probability vs Odds: The Math

Probability is expressed as a percentage from 0% (will never happen) to 100% (will certainly happen). These percentages can also be expressed as a decimal from 0 to 1; to convert a percentage to a decimal, move the decimal point two places to the right. For example, 100.00% becomes 1.00 as a decimal. **You can look at a probability as a number that represents the chance or likelihood an event will happen. **

**Chances **are almost always expressed as a percentage; you can think of them as probabilities expressed in a scale “by the hundred”. In other words, the measurement scale for chances and probabilities is different. For example, if the probability of an event happening is 1/4, then the chance of the event happening is 25% (1/4 times 100 percent). Therefore, a chance of 25% literally means that 25 of every one hundred of this particular event would likely happen [1].

Odds is the probability an event will happen, divided by the probability an event will not happen. As a formula:

Odds = p / (1 – p),

where *p* is the probability (“chance”) of an event happening.

As an example, let’s say you buy a scratch off lottery ticket with stated odds of 1:5 that you’ll win a prize. That means you have one chance of winning vs. five chances of *not *winning.

To convert odds to probability:

- Place the odds of winning in the numerator of a fraction.
- Place the odds of winning and losing in the denominator.
- Using the above example, odds of 1/5 becomes a probability of 1/(5+1) – 1/6.

You can also convert more without using the formula, if you understand what the odds represents. Odds of 1 to 5 means “one for and five against”. In other words, out of six possible chances (1 + 5), you’ll win once. As a percentage, that’s 1/6; this is our probability. If we put that probability into the formula we get:

Odds = (1/6) / (1 – (1/6)) = (1/6) / (5/6) = 1/5.

Odds are usually not stated in fractional form though; it’s more common to say 1:5 or 1 to 5.

## Chance vs Probability vs Odds: References

Fulton, L. et al. (2012). Confusion Between Odds and Probability, a Pandemic? Journal of Statistics Education, Volume 20, Number 3

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