CONDORCET. 405 



. . 2 



babilite rooyenne; — r- exprimera de meine celle des 45 aiitras evene- 



mens ayaut cliacun la probabilite y— : ainsi la probabilite propre de 



I'evenemeiit sera - . 



o 



Condorcet himself observes that it may appear singular that 

 the result in this case is less than that which was obtained in 

 Ai't. 74;0 ; so that a man is less trustworthy when he merely says 

 that he has seen the same card drawn twice, than when he tells us 

 in addition what card it was that he saw drawn twice. Condorcet 

 tries to explain this apparent singularity; but not with any ob- 

 vious success. 



The singularity however seems entirely to arise from Con- 

 dorcet 's own arbitrary choice ; the rule which he himself lays do^\ai 

 requires him to estimate la prohabilite moyenne de tons les autres 

 evenemens, and he estimates this mean probability differently in 

 the two cases, and apparently without sufficient reason for the dif- 

 ference. 



744. Condorcet's next example is as follows : We are told that 

 a person with two dice has five times successively thrown higher 

 than 10 ; find the prohabilite lyropre. With two dice the number 

 thrown may be 2, 3, ... up to 12 ; the respective probabilities are 



86' 36' 36' 36' 36' 36' 36' 36' 36' 36' 36* 



_, , , 1 c , . 11 X 12 X 13 X 14 X 15 ,, ^ . 

 The whole number ol events is r^ , that is 



L? 



3003 ; and of these only 6 belong to the proposed combination. 



1 



Since the probability of these 6 throws is :r^ their mean proba- 

 bility is -^ -^ . The mean probability of the other throws will 



u X J-^ 



11^ . 2997 



he ^gc)- X 12^ * ^^^^^ ^^^® prohahiliie propre is g >< ir + 2997 * 



It is obvious that all this is very arbitrary. Wlien Condorcet 

 says there are 6 throws belonging to the proposed combination he 

 means that all the throws may be 12, or all 11, or four 12 and one 

 11, or three 12 and two 11, . . . And he says the mean probability is 



