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
| Probability is a measure of the likelihood of an event to occur. Since probability is a quantified measure, it has to be developed with the mathematical background. Specifically, this mathematical build of the probability is known as the probability theory. | Statistics is the discipline of collection, organization, analysis, interpretation, and presentation of data. Most statistical models are based on experiments and hypotheses, and probability is integrated into the theory, to explain the scenarios better. |
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/.
Probability Isn’t Just Theory
Probability isn’t just theory — it runs the modem world. From predicting outcomes to managing uncertainty,
probability powers:
- Data science & statistics — making sense of data
- Artificial intelligence & machine learning — decision-making under uncertainty
- Finance & stock markets — risk returns, and volatility
- Medicine & genetics — diagnosis, trials, and predictions
- Weather forecasting — modeling future conditions
- Gaming & simulations — randomness and fairness
- Autonomous systems — safety and real-time decisions
Every prediction, every model, every intelligent system begins with probability.
Pi Mathematica. “”The best probability course on the internet—taught by Harvard University”” Instagram. Accessed January 27, 2026. https://www.instagram.com/reels/DT-9ReqEs-2/.
Recommended
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.
Additional Reading
Henshaw, Glenn. “Probability Theory By Example (Part 2)”. 2019. Medium. https://ghenshaw-work.medium.com/probability-theory-by-example-part-2-62c30057820a.
“Probability Concepts Explained: Introduction”. 2018. Medium. https://towardsdatascience.com/probability-concepts-explained-introduction-a7c0316de465.
Taylor, Kylie. “The Difference Between Probability And Statistics”. 2023. Medium. https://kylie-taylor.medium.com/the-difference-between-probability-and-statistics-dd64ffe73964.
Probability: We know the source of our data and want to calculate an outcome.
Statistics: We know an outcome and want to learn the source of our data.
Videos
Probability theory helps us understand chance. It shows how likely something is to happen, from events that are impossible to events that are certain. For example, it can help explain the chance of flipping heads on a coin, rolling a six on a die, or getting rain tomorrow. It is used to make predictions, study risk, and understand uncertainty in everyday life.
This video provides a straightforward introduction to probability theory, explaining how it measures the likelihood of events, from impossible (zero) to certain (one) (0:18-0:36).
Here are the key concepts covered:
Outcomes & Sample Space: An outcome is a single possible result (e.g., landing on a specific number on a roulette wheel), while the sample space is the list of all possible outcomes (1:34-3:54).
Events & Calculation: An event is a specific set of outcomes you are interested in. If all outcomes are equally likely, probability is calculated as the number of favorable outcomes divided by the total number of outcomes (2:21-5:32).
Independence & Fallacies: Independent events (like coin flips or roulette spins) do not affect each other. The video warns against the gambler’s fallacy, which is the false belief that a past streak influences future random results (6:22-9:32).
And/Or Logic: The video explains intersections (and – both events occur) and unions (or – at least one event occurs) (9:57-12:22).
Casino Math: Casinos profit using the house edge—a small, long-term mathematical advantage. Even if players win in the short term, the law of large numbers ensures that the casino’s tiny advantage guarantees profits over thousands of games (12:24-16:52).
The featured image on this page is from the article “Probability Theory By Example (Part 1)”. 2019. Medium. https://ghenshaw-work.medium.com/probability-theory-by-example-part-1-1e409d1d9f4a.