# Probability - The Formal Theory Of Probability, Interpretations Of Probability, Some Recent Developments, Some Applications Of Probability

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probabilistic notion century pierre

"Probability is the very guide of life," Bishop Butler wrote in 1736. Probability judgments of the efficacy and side effects of a pharmaceutical drug determine whether it is approved for release to the public. The outcome of a civil trial hinges on the jurors' opinions about the probabilistic weight of evidence. Geologists calculate the probability that an earthquake of a certain intensity will hit a given city, and engineers accordingly build skyscrapers with specified probabilities of withstanding such earthquakes. Probability undergirds even measurement itself, since the error bounds that accompany measurements are essentially probabilistic confidence intervals. We find probability wherever we find uncertainty—that is, almost everywhere in our lives.

It is surprising, then, that probability arrived comparatively late on the intellectual scene. To be sure, a notion of randomness was known to the ancients. Epicurus, and later Lucretius, believed that atoms occasionally underwent indeterministic swerves. The twelfth-century Arabic philosopher Averroës's notion of "equipotency" might be regarded as a precursor to probabilistic notions. But probability theory was not conceived until the seventeenth century, in the correspondence between Pierre de Fermat and Blaise Pascal and in the Port-Royal Logic. Over the next three centuries, the theory was developed by such authors as Christian Huygens, Jacob Bernoulli, Thomas Bayes, Pierre Simon Laplace, the Marquis de Condorcet, Abraham de Moivre, John Venn, William Johnson, and John Maynard Keynes. Arguably, the crowning achievement was Andrei Kolmogorov's axiomatization in 1933, which put probability on a rigorous mathematical footing.

## Additional Topics

In Kolmogorov's theory, probabilities are numerical values that are assigned to "events." The numbers are non-negative; they have a maximum value of 1; and the probability that one of two mutually exclusive events occurs is the sum of their individual probabilities. Stated more formally, given a set and a privileged set of subsets F of, probability is a function P from F to th…

The classical interpretation, historically the first, can be found in the works of Pascal, Huygens, Bernoulli, and Leibniz, and it was famously presented by Laplace (1814). It assigns probabilities in the absence of any evidence and in the presence of symmetrically balanced evidence. In such circumstances, probability is shared equally among all the possible outcomes—the so-called principle…

Since the late twentieth century, some subjectivists have canvased further desiderata on credences. For example, we might evaluate credences according to how closely they match the corresponding relative frequencies, according to how well "calibrated" they are. Also under consideration are "scoring rules" that refine calibration. Various subjectivists believe that ratio…

Probability theory thus continues to be a vigorous area of research. Moreover, its advances have myriad ramifications. Probability is explicitly used in many of our best scientific theories, for example, quantum mechanics and statistical mechanics. It is also implicit in much of our theorizing. A central notion in evolutionary biology is "fitness," or expected number of offspring. Ps…

Butler, Joseph. Analogy of Religion. 1736. Reprint, New York: Frederick Ungar, 1961. Carnap, Rudolf. Logical Foundations of Probability. Chicago: University of Chicago Press, 1950. De Finetti, Bruno. "La Prévision: Ses Lois Logiques, Ses Sources Subjectives." Annales de l'Institut Henri Poincaré 7 (1937): 1–68. Translated as "Foresight: Its Logical Laws…

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