If I have a fair coin (parameter value) then the probability that it will come up heads is

0.5.

If I flip a coin100times and it comes up heads52times then it has ahigh likelihood of being fair(the numeric value of likelihood potentially taking a number of forms).

stats.stackexchange.com/a/2642

The difference between probability and likelihood is closely related to the difference between probability and statistics.

In a sense probability and statistics concern themselves with problems that areopposite or inverse to one another.

stats.stackexchange.com/a/2649

The distinction between probability and likelihood is fundamentally important:

probabilityattaches topossible results;likelihoodattaches tohypotheses.

C. Randy Gallistel - «Bayes for Beginners: Probability and Likelihood» (2015)

Probability quantifies anticipation (of outcome), likelihood quantifies trust (in model).

stats.stackexchange.com/a/56035

Although a likelihood function might look just like a probability density function, it’s

fundamentally different:

- A
probability density functionis a function ofx, your data point, and it will tell youhow likely it is that certain data points appear.- A
likelihood function, on the other hand, takes the data set as a given, and represents thelikeliness of different parametersfor your distribution.

Unlike probability density functions,

likelihoods aren’t normalized.

The area under their curves does not have to add up to 1.

statisticshowto.datasciencecentral.com/likelihood-function#post-47406