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