368 CONDORCET. 



we see the meaning which Condorcet should have expressed, and 

 although it is almost superfluous to attempt to correct what is 

 nearly unintelligible, it would seem that paires should be changed 

 to impaires. 



683. Condorcet's problem may be generalised. We may ask 

 what is the probability that in r trials the event will happen 

 p times in succession before it fails q times in succession. In this 

 case instead of (7) we shall have 



'^{7i) = <i> {n) — e^~^ [(f> {n — g -^ 1) — e^lr {n - q)] ; 

 instead of (9) we shall have 



(l){r)-'e^(j>{r-q)=v''{l-e') 



+ v""-' e {(/) (r -p) - e^"' <f> (r -p-q + l)\ 



+ V ^"' e {(^ (r -^ + 1 ) - e«-' (f> {r -^- q+ 2)] 



+ ... 



and instead of (10) we shall have 



^^" (1 - e^ 



684. We will introduce here two remarks relating to that 

 part of Condorcet's Preliminary Discourse which bears on his 

 ninth Hypothesis. 



On page xxxvi. he says, 



...c'est qu'en supposant que I'on connoisse le nombre des decisions 

 et la pluralite de chacune, on pent avoir la somme des pluralites obte- 

 nues contre I'opinion qui I'emporte, plus graiide que celle des pluralites 

 conformes a cet avis. 



This is a specimen of a kind of illogical expression which is 

 not uncommon in Condorcet. He seems to imply that the result 

 depends on our knoiving something, whereas the result might 

 happen quite independently of our knowledge. If he will begin 

 his sentence as he does, his conclusion ought to be that we may 

 have a certain result and know that lue have it. 



On page xxxvii. he alludes to a case which is not discussed 

 in the Essay. Suppose that a question is submitted to a series 



