The grand object of seeking to estimate the probability of future events from past experience, seems to have been entertained by James Bernoulli and De Moivre, at least such was the opinion of Condorcet; and Bernoulli may be said to have solved one case of the problem.[173] The English writers Bayes and Price are, however, undoubtedly the first who put forward any distinct rules on the subject.[174] Condorcet and several other eminent mathematicians advanced the mathematical theory of the subject; but it was reserved to the immortal Laplace to bring to the subject the full power of his genius, and carry the solution of the problem almost to perfection. It is instructive to observe that a theory which arose from petty games of chance, the rules and the very names of which are forgotten, gradually advanced, until it embraced the most sublime problems of science, and finally undertook to measure the value and certainty of all our inductions. [173] Todhunter’s *History*, pp. 378, 379. [174] *Philosophical Transactions*, [1763], vol. liii. p. 370, and [1764], vol. liv. p. 296. Todhunter, pp. 294–300. *Fortuitous Coincidences.* We should have studied the theory of probability to very little purpose, if we thought that it would furnish us with an infallible guide. The theory itself points out the approximate certainty, that we shall sometimes be deceived by extraordinary fortuitous coincidences. There is no run of luck so extreme that it may not happen, and it may happen to us, or in our time, as well as to other persons or in other times. We may be forced by correct calculation to refer such coincidences to a necessary cause, and yet we may be deceived. All that the calculus of probability pretends to give, is *the result in the long run*, as it is called, and this really means in *an infinity of cases*. During any finite experience, however long, chances may be against us. Nevertheless the theory is the best guide we can have. If we always think and act according to its well-interpreted indications, we shall have the best chance of escaping error; and if all persons, throughout all time to come, obey the theory in like manner, they will undoubtedly thereby reap the greatest advantage.