CHAPTER XVIII. 



OF THE CALCULATION OF CHANCES. 



1. " PROBABILITY/' says Laplace,* " has reference partly 

 to our ignorance, partly to our knowledge. We know that 

 among three or more events, one, and only one, must happen ; 

 but there is nothing leading us to believe that any one of 

 them will happen rather than the others. In this state of in- 

 decision, it is impossible for us to pronounce with certainty 

 on their occurrence. It is, however, probable that any one of 

 these events, selected at pleasure, will not take place ; because 

 we perceive several cases, all equally possible, which exclude 

 its occurrence, and only one which favours it. 



" The theory of chances consists in reducing all events of 

 the same kind to a certain number of cases equally possible, 

 that is, such that we are equally undecided as to their existence; 

 and in determining the number of these cases which are 

 favourable to the event of which the probability is sought. 

 The ratio of that number to the number of all the possible 

 cases, is the measure of the probability ; which is thus a frac- 

 tion, having for its numerator the number of cases favourable 

 to the event, and for its denominator the number of all the 

 cases which are possible." 



To a calculation of chances, then, according to Laplace, two 

 things are necessary : we must know that of several events 

 some one will certainly happen, and no more than one ; and 

 we must not know, nor have any reason to expect, that it 

 will be one of these events rather than another. It has been 

 contended that these are not the only requisites, and that 

 Laplace has overlooked, in the general theoretical statement, 

 a necessary part of the foundation of the doctrine of chances. 



* JEssai Philosopkique sur les Probabilites, fifth Paris Edition, p. 7. 



