276 ELEMENTARY ILLUSTRATIONS. [CHAP. XVIII. 



CHAPTER XVIII. 



ELEMENTARY ILLUSTRATIONS OF THE GENERAL METHOD IN PROBA- 

 BILITIES. 



1 TT is designed here to illustrate, by elementary examples, 

 -- the general method demonstrated in the last chapter. 

 The examples chosen will be chiefly such as, from their sim- 

 plicity, permit a ready verification of the solutions obtained. 

 But some intimations will appear of a higher class of problems, 

 hereafter to be more fully considered, the analysis of which 

 would be incomplete without the aid of a distinct method deter- 

 mining the necessary conditions among their data, in order that 

 they may represent a possible experience, and assigning the cor- 

 responding limits of the final solutions. The fuller consideration 

 of that method, and of its applications, is reserved for the next 

 chapter. 



2. Ex. 1. The probability that it thunders upon a given 

 day is p 9 the probability that it both thunders and hails is q 9 but 

 of the connexion of the two phenomena of thunder and hail, no- 

 thing further is supposed to be known. Required the probability 

 that it hails on the proposed day. 



Let x represent the event It thunders. 

 Let y represent the event It hails. 



Then xy will represent the event It thunders and hails ; and 

 the data of the problem are 



Prob. x = p, Prob. xy = q. 



There being here but one compound event xy involved, assume, 

 according to the rule, 



xy = u. (1) 



Our data then become 



Prob. x = p, Prob. u = q ; (2) 



,nd it is required to find Prob. y. Now (1) gives 



a 



