2 CONDORCET. 



I (1 — x) xdx 

 ^ ^ 



I {1 — x) dx 



2 

 which is ^ . If the value of x lies between a and 1 the mean pro- 

 o 



bability is found in the same way to be • — ^ — . 



This example is interesting, but some parts of the investiga- 

 tions connected with it are very obscure. 



As in other parts of his book Condorcet draws a very in- 

 significant inference from his difficult investigations. He says, 

 page 303, 



On voit done combien il est important, non-seulement que les 

 hommes soient eclaires, mais qu'en meme temps tous ceux qui, dans 

 I'opinion publique, passent pour instruits ou liabiles, soient exempts de 

 prejuges. Cette deriiiere condition est meme la plus essentielle, puisqu'il 

 paroit que rien ne peut remedier aux inconveniens qu'elle entraine. 



721. Besides the Essai Condorcet wrote a long memoir on the 

 Theory of Probability, which consists of six parts, and is published 

 in the volumes of the Hist de V A cad.... Paris, for the years 1781, 

 1782, 1783, and 1784. 



The first and second parts appear in the volume for 1781 ; 

 they occupy pages 707 — 728. The dates of publication of the 

 volumes are as usual later than the dates to which the volumes 

 belong ; the portion of the memoir which appears in the volume 

 for 1781 is said to have been read on August 4th, 1784. 



722. The first part of the memoir is entitled Reflexions sur la 

 regie generate qui prescrit de prendre pour valeur d'lm evenement 

 incertain, la prohahilite de cet evenement, multipliee par la valeur de 

 Vevenement en lui-meme. 



Suppose that p represents the probability that an event will 

 happen, and that if the event happens a person is to receive a sum 

 of money denoted by a ; then the general rule to which Condorcet 

 refers is the rule which estimates the person's advantage at the 

 sum pa. On this rule Condorcet makes some remarks ; and these 

 remarks arc also given in substance in the Essai, in pages 



