The differences between likelihood and probability — simply explained with examples

The words’ likelihood’ and ‘probability’ are often confusing for many people, and as such, they require proper clarification. It is common to use the word ‘probability’ when thinking about the possibility of an event occurring. However, it is essential to note that while the two terms may seem similar, they have a partial overlap but cannot be used interchangeably.

In fact, ‘likelihood’ refers to the degree of belief or expectation that something will happen, while ‘probability’ refers to the ratio of favorable outcomes to the total number of possible outcomes. Therefore, it is crucial to understand the subtle differences between these two concepts in order to use them correctly in different contexts. For instance, you would use probability when calculating the chances of winning a lottery. Still, you would use likelihood when assessing the likelihood of a specific event based on available evidence.

“The likelihood function ( likelihood) represents the probability of random variable realizations conditional on particular values of the statistical parameters” (ref.).

The likelihood is the chance, the possibility of doing or achieving something, and the condition that can ensure success. Probability is a degree, a relative measure, or a quantitative assessment of the possibility of an event occurring.

Let’s try to understand probability and likelihood from a probability theory.