What Are Probabilities?

It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge.

- Pierre-Simon Laplace, Philosophical Essay on Probabilities

Podcast of the Day

Melvyn Bragg and guests discuss the strange mathematics of probability where heads or tails is a simple question with a far from simple answer. Gambling may be as old as the hills but probability as a mathematical discipline is a relative youngster. Probability is the field of maths relating to random events and, although commonplace now, the idea that you can pluck a piece of maths from the tumbling of dice, the shuffling of cards or the odds in the local lottery is a relatively recent and powerful one. It may start with the toss of a coin but probability reaches into every area of the modern world, from the analysis of society to the decay of an atom.

Listen to the In Our Time episode on Probability

Video of the Day

Short Article of the Day

Our world view and resultant actions are often driven by a simple theorem, devised in secret more than 150 years ago by a quiet English mathematician and theologian, Thomas Bayes, and only published after his death.

Bayes’ Theorem was famously used to crack the Nazi Enigma code during World War II, and now manages uncertainty across science, technology, medicine and much more.

So how does it work?...

Continue reading Lee & King's article: Bayes’ Theorem: the maths tool we probably use every day, but what is it?

Further Reading

Probability is the measure of the likelihood that an event will occur. See glossary of probability and statistics. Probability is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility 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%).

These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in such areas of study as mathematics, statistics, finance, gambling, science (in particular physics), artificial intelligence/machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems...

Continue reading the Wikipedia article on Probability

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Related Topics

If you’re interested in probability theory, check out some of the following related topics for more resources:

 Correlation and CausationForecasting | Game Theory | Mathematics | Randomness

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