History of the Mathematical Theory of Probability from the Time of Pascal to That of Laplace (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1865 Excerpt: ...if we suppose that a, b, c, d, ... are connected by a certain law which he gives, namely, 1-a-b-c-d-e-...----.-, l + (m-l)p where p is a small fraction, and m--1 is the number of the quantities a, b, c, d, e, ... Again he shews that the same result holds if we merely assume that a, b, c, d, e... form a continually diminishing series. We say that this appears to be a work of supererogation for D'Alembert, because we consider that the infinite result was the only supposed difficulty in the Petersburg Problem, and that it was sufficient to remove this without shewing that the series substituted for the ordinary series consisted of terms continually decreasing. But D'Alembert apparently thought differently; for after demonstrating this continual decrease he says, En voila assez pour faire voir que les termes de l'enjeu vont en Jimimiant d& le troisieme coup, jusqu'au dernier. Nous avons prouv6 d'ailleurs que l'enjeu total, somme de ces termes, est fini, en supposant raeme le nombre de coups infini. Ainsi le rcsultat de la solution que nous donnons ici du probleme de Petersbourg, n'est pas sujet a la difficulty insoluble des solutions ordinaires. 533. We have one more contribution of D'Alembert's to our subject to notice; it contains errors which seem extraordinary, even for him. It is the article Cartes in the Encyclopedie Methodique. The following problem is given, Pierre tient huit cartes dans ses mains qui sont: un as, un deux, un trois, un quatre, un cinq, un six, un sept et un huit, qu'il a melees: Paul parie que les tirant l'une apres l'autre, il les devinera a mesure qu'il les tirera. L'on demande combien Pierre doit parier contre un que Paul ne reussira pas dans son enterprise? It is correctly determined that Paul's chan...