Common questions about Probability

Short answers, pulled from the story.

What did the word probability mean in sixteenth-century Europe?

In sixteenth-century Europe, the word probability measured the weight of a witness's authority rather than chance. A nobleman's testimony carried more probability than a peasant's because the term derived from the Latin probitas, meaning probity or moral uprightness. This ancient legal definition stood in stark contrast to the modern mathematical concept where probability quantifies the likelihood of an event occurring on a scale from zero to one.

When did the scientific study of probability emerge and who started it?

The scientific study of probability emerged in the middle of the seventeenth century, specifically marked by the correspondence between Pierre de Fermat and Blaise Pascal in 1654. This correspondence solved problems posed by gamblers who wanted to know how to divide stakes fairly when a game was interrupted. Before this moment, the term probable simply meant approvable or sensible, applied to opinions and actions that reasonable people would undertake.

Who developed the method of least squares and when was it published?

Adrien-Marie Legendre developed the method of least squares in 1805. Robert Adrain, an Irish-American writer, independently deduced the law of facility of error in 1808. Pierre-Simon Laplace followed with two laws of error in 1774 and 1778, the second of which became known as the normal distribution or the Gauss law.

What is the difference between frequentists and Bayesians in probability theory?

Frequentists claim that probability denotes the relative frequency of an outcome when an experiment is repeated indefinitely, existing as an objective property of the world. Subjectivists, led by the Bayesian interpretation, argue that probability is a degree of belief, a price at which one would buy or sell a bet based on available evidence. A Bayesian agent uses a prior probability distribution to represent expert knowledge, which is then updated by a likelihood function to produce a posterior probability.

When did Albert Einstein write to Max Born about God playing dice?

Albert Einstein wrote to Max Born in 1926 that he was convinced God does not play dice. He famously rejected the probabilistic nature of quantum mechanics, which exhibits a random character that cannot be explained by hidden variables. The Copenhagen interpretation of quantum mechanics relies on the objective wave function to describe probabilities of observation, with the outcome explained by a wave function collapse.

When was the modern theory of probability formalized and by whom?

The modern theory of probability was formalized in 1931 by Andrey Kolmogorov, who established a framework based on measure theory that remains the standard today. Kolmogorov's formulation interprets sets as events and probability as a measure on a class of sets, providing a rigorous mathematical foundation for the field. This approach was paralleled by the Cox formulation, which takes probability as a primitive and emphasizes the construction of a consistent assignment of probability values to propositions.

Read the full story about Probability →