Probability once meant a witness's social standing
Today a fair coin sits at one half. Centuries ago, Latin probabilitas could mean a witness's legal weight, often tied to nobility. Modern chance instead weighs evidence through counting, frequencies, or degrees of belief—and still splits objectivists from subjectivists.
Probability numbers how likely events are, always between zero and one, sometimes written as a percentage. A fair coin gives heads and tails equal chance, so each is one half. Theoretical settings count favorable outcomes over all outcomes: two tosses yield four pairs, so double heads is one fourth and at least one head is three fourths. Axiomatic probability theory carries those ideas into statistics, science, finance, gambling, artificial intelligence, and philosophy.
Objectivists treat numbers as features of the world. Frequentists read long-run relative frequency; propensity views stress a single trial's tendency. Subjectivists treat probability as degree of belief, sometimes as a betting price for a unit payoff. Bayesian practice updates prior expert belief with a likelihood from data to a posterior. Similar priors tend to converge by Aumann's agreement theorem; wildly different priors need not.
Richard Jeffrey noted that before the mid-seventeenth century, probable meant approvable by sensible people. Cardano showed odds as favorable over unfavorable. Fermat and Pascal's 1654 correspondence, Huygens in 1657, Jakob Bernoulli's Ars Conjectandi of 1713, and Abraham de Moivre's Doctrine of Chances of 1718 made the subject mathematical. Laplace proposed error laws in the 1770s; the second, exponential in the squared error, became the normal or Gauss law—despite jokes about Gauss's infancy.
Legendre published least squares in 1805; Gauss and others proved related results. Andrey Markov introduced Markov chains in 1906; Andrey Kolmogorov built measure-theoretic probability in 1931. Kolmogorov and Cox formalisms differ in primitives yet yield largely the same laws. Applications span insurance, regulation, biology, casino design, and product reliability that shapes warranties.
Source: Probability
