CONDORCET. 381 



He continues in the usual way. If the first hypothesis be true 



tn -j- 1 



the probability of another A is ; if the second hypo- 



^ "^ 771 + W + 2 ^^ 



thesis be true the probability of another ^ is ^ . Thus finally the 

 probability in favour of A is 



P+ (3 V^ + ^ + 2 ^2 ^J- 

 Similarly the probability in favour of N is 



1 f ?2 + 1 



-^p^\q\ 



It should be noticed that in this solution it is assumed that 

 the two hypotheses were equally probable d yrioriy which is a very 

 important assumption. 



700. Suppose that m + n is indefinitely large ; if m = n it may 

 be shewn that the ratio of P to Q is indefinitely small ; this ratio 

 obviously increases as the difference of m and n increases, and is 

 indefinitely large when m or n vanishes. Condorcet enunciates 

 a more general result, namely this ; if we suppose m = an and 

 n infinite, the ratio of P to Q is zero if a is unity, and infinite 

 if a is greater or less than unity. Condorcet then proceeds, 



Ainsi supposons m et n donnes et inegaiix ; si on continue d' observer 

 les evenemens, et que m et n conservent la meme proportion, on parvi- 

 endra a une valeur de m et de n, telle qu'on aura une probabilite anssi 

 grande qu'on voudra, que la probabilite des evenemens A et J^ est con- 

 stante. 



Par la meme raison, lorsque m et n sont fort grands, leur difference, 

 quoique tres-grande en elle-meme, pent etre assez petite par rapport au 

 nornbre total, pour que Ton ait une tres-grande probabilite que la pro- 

 babilite d'avoir A ou iV^n'est pas constante. 



The second paragi^aph seems quite untenable. If in a very 

 large number of trials A and N had occurred very nearly the same 

 number of times we should infer that there is a constant proba- 

 bility namely ^ for A and ^ for N. It is the more necessary to 



