400 CONDORCET. 



are as arbitrary as those which we have ah*eady given, and not 

 fully intelligible ; see his pages 550 — 553. 



735. The fifth part of Condorcet's memoir is entitled Sur la 

 prohahilite desfaits extraordinaires. 



Suppose that p is the probability of an event in itself; let t 

 denote the probability of the truth of a certain witness. This wit- 

 ness asserts that the event has taken place ; required the proba- 

 bility that the event did take place, and that it did not. The 

 required probabilities are 



Pt and (1 -P) (1 - 



jyt+{\-p){\-t) "^ pt^(l-p][\-t)- 



Condorcet gives these formulae with very little explanation. 



The application of these formulae is not free from difficulty. 

 Suppose for example a trustworthy witness asserts that one ticket 

 of a lottery of 10000 tickets was drawn, and that the number of 



the ticket drawn was 297. Here if we put p = we obtain 



such a very small value of the truth of the witness's statement that 

 we lose our confidence in the formula. See Laplace Theorie...des 

 Proh. pages 446 — 451. De Morgan, Cambridge Philosophical 

 Transactions, Vol. ix. page 119. 



736. Condorcet makes remarks on two points, namely the 

 mode of estimating p and the mode of estimating t He recurs to 

 the former point in the sixth part of his memoir, and we shall give 

 an extract which will shew the view he advocated in his fifth part, 

 and the view which he advocated in his sixth part. 



With respect to the second point Condorcet's chief remark is 

 that the probability of a witness is not the same for all facts. If 

 we estimate it at u for a simple fact, then we should estimate it at 

 v^ for a compound fact consisting of two simple facts, and so on. 

 One witness however may be as capable of observing a compound 

 fact consisting of two or more simple facts as another is of observ- 

 ing a simple fact. 



737. The sixth part of Condorcet's memoir is entitled Appli- 



