# Probability

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

"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.