Difference Between Probability and Odds

Probability vs Odds

Real life is full of incidents with uncertainty. The terms probability and odds measure one’s belief in the occurrence of a future event. It may confuse since both ‘Odds’ and ‘probability’ are related to the potential that event occurs. However, there is a difference. Probability is a broader mathematical concept. However odds is another method for calculating probability.


In classical theory, Probability is used to calculate the likelihood that something will happen; as a ratio, the number of desired outcomes to the total number of possible outcomes, which is expressed as a number between 0 to 1, where 0 implying “impossible” and 1 implying “certain” or “sure”. This is also expressed as the “chance” of occurrence of the event. In this, case the scale is from 0% to 100%.

For an experiment, whose outcomes are equally likely, the probability of an event E, denoted by P(E), can be expressed mathematically as: the number of outcomes favorable to E divide by the total number of possible outcomes.

For example, if we have 10 marbles in a jar, 4 blue and 6 green, then the probability of drawing a green is 6/10 or 3/5. There are 6 chances of getting a green marble and total number of chances of getting a marble is 10. The probability of drawing a blue is 4/10 or 2/5.


The Odds of an event is an alternative way of expressing the likelihood of its occurrence. That can be expressed as a ratio of the number of favorable outcomes to the number no of unfavorable outcomes, i.e. odds = number of favorable outcomes: number of unfavorable outcomes.

Since there are 6 chances of you picking a green, and 4 chances of picking a red, the odds is 6 : 4 in favor of picking a green. The odds is 4 : 6 in favor of picking a blue.

The idea of odds comes from gambling. Even probability is easy to work mathematically, but harder to apply in gambling. That’s why we have two different ways to express the concept. If we know the odds in favor of an event, the probability is just the odds divided by one plus the odds. Odds depends on the probability. Odds can be calculated using probability. Probability can also be converted into an odd. Simply, the odds in favor of an event is division of probability of that event by one minus the probability: i.e. Odds = Probability/(1-Probability). If the odds in favor of an event is known, the probability is just the odds divided by one plus the odds: i.e. Probability= Odds/(1+Odds).

What is the difference between Probability and Odds?

• Probability is expressed as a number between 0 and 1, while Odds is expressed as a ratio.

• Probability ensures that an event will occur, but Odds is used to find out whether the event will ever occur.