The Difference Between Probability and Odds

In everyday conversations people tend to use probability and odds interchangeably when describing the likelihood of an outcome. However, mathematically speaking, they are different; probability in percentage terms and odds of an outcome in the form of a ratio, respectively.

Simple probability of event A occurring is mathematically defined as:

P(A) = \frac{Number \ of \ Event \ A}{Total \ Number \ of \ Events}

Odds calculation – Generally, odds are expressed as the ratio of favorable outcomes to unfavorable outcomes. To find an odds ratio from a given probability, first express the probability as a fraction. Subtract the numerator (1) from the denominator (6) : 6 – 1 = 5 . The answer is the number of unfavorable outcomes. Odds can then be expressed as 1 : 5 – the ratio of favorable to unfavorable outcomes.

Odds\_Favor(A) = \frac{P(A)}{1 - P(A)}

So for example, the probability of rolling a 3 on a single die is 1/6 or 16.67%. The odds are 1:5.


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