100 Years Ago This Month in The American Mathematical Monthly

It is a strange anomaly that that branch of mathematics, known as the theory of probability, which rests upon the fewest, simplest, and least controvertible fundamental principles, which demands practically no mathematical prerequisites for its pursuit, which throughout occupies itself with innumerable interesting and important problems that even the layman can understand, should be, at the same time, that branch of mathematics which has presented the greatest number of pitfalls to its most illustrious devotees. [. . . ] Cardan, as will be shown presently, may be said to have inaugurated the study with a mistaken solution; Pascal, another pioneer of the subject, committed a fallacy in his problem of points involving three players; Leibnitz fell into error in thinking that a throw of twelve with two dice is as probable as a throw of eleven. D’Alembert stumbled time and again when dealing with probabilities. James Bernoulli, in his Ars Conjectandi, recorded two erroneous solutions of his nineteenth problem which occurred to him before he obtained its true solution.