Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes (“heads” and “tails”) are both equally probable; the probability of “heads” equals the probability of “tails”; and since no other outcomes are possible, the probability of either “heads” or “tails” is 1/2 (which could also be written as 0.5 or 50%).

“Probability – Wikipedia”. 2021. en.wikipedia.org. https://en.wikipedia.org/wiki/Probability.

## Probability vs Statistics

What is the difference between Probability and Statistics?

• Probability and statistics can be considered two opposite processes, or rather two inverse processes.
• Using probability theory, the randomness or uncertainty of a system is measured by means of its random variables. As a result of the comprehensive model developed, the behaviour of the individual elements can be predicted. But in statistics, a small number of observations is used to predict the behaviour of a larger set whereas, in probability, limited observations are selected at random from the population (the larger set).
• More clearly, it can be stated that using probability theory the general results can be used to interpret individual events, and the properties of the population are used to determine the properties of a smaller set. The probability model provides the data regarding the population.
• In statistics, the general model is based on specific events, and the sample properties are used to infer the characteristics of the population. Also, the statistical model is based on the observations/ data.

“Difference Between Probability And Statistics | Compare The Difference Between Similar Terms”. 2012. Compare The Difference Between Similar Terms. https://www.differencebetween.com/difference-between-probability-and-vs-statistics/.

Kunin, Daniel. 2021. “Seeing Theory”. seeing-theory.brown.edu. https://seeing-theory.brown.edu/.

An interactive visual introduction to probability and statistics. It currently covers six chapters: basic probability, compound probability, probability distributions, frequentist interference, Bayesian interference, and regression analysis. Each chapter contains interactive exercises to help visualize and understand the information.

“Probability Tutorial”. 2022. stattrek.com. https://stattrek.com/tutorials/probability-tutorial.

Applied researchers make decisions under uncertainty. Probability theory makes it possible for researchers to quantify the extent of uncertainty inherent in their conclusions and inferences.