40G CONDORCET. 



But if we consider tlie different orders in which these 



6x 12^* 



throws can occur we may say that the whole number is 2^ and the 



1 / 1 2 \^ 1 



mean probabihty ^ ( 35 + 35 j ^ ^^^^^ ^^ 2^2" ' 



Again let us admit that there are 8003 cases in all, and that of 

 these only 6 belong to the proposed combination. The other 

 2997 cases form two species, namely those in which every throw is 

 below 11, and those in which some throws are below 11 and the 



ir 



others above 10 ; when Condorcet takes -—^ — -^ as the mean 

 probability, he forgets this division of species and only con- 

 siders the first species. He should take ^ [ 1 — ^-^1 instead 



ir 



of 



2997 X 12' • 



7-i5. Suppose two classes of events A and B; let the pro- 

 bability of an A he a and the probability of a i> be ^ ; let there 

 be m events A and n events B. The ]^'t^obabilite projore of an 

 assigned event of the class B will be, according to Condorcet's 

 practice, 



h ^1 . • (m + n— 1) h 



- ""-- ■■ " ^ , that IS ; -: —, . 



ma 4- {ii — l)u -. ma + {^ni + Zr — 'I) 



m -\- n—1 



21) 



If m and n be equal and very large this becomes ^ . If 



a -p ou 



we suppose h extremely small and consequently a very nearly 



unity we obtain 2h as an approximate value. 



716. Condorcet proceeds to apply his doctrine to the credi- 

 bility of two statements in the History of Home. He says, 



Je vais maintenant essay er de faire a nne question de critique 

 rapplication des principes que je viens d'etablir. Newton paroit etre 

 le premier qui ait eu I'idee d'appliquer le calcul des probabilites a la 

 critique des faits. II propose, dans son ouvrage sur la clironologie, 

 d'employer la connoissance de la durce moyenne des generations et des 

 regncs, telle que I'experience nous la donue, soit pour fixer d'une 

 manicre du moins approchee, des points de clironologie fort incertains, 



