SECT. 2.] The Rules of Inference in Probability. 169 



in 100 live to over sixty, 35.4 in 100 die before they are 

 ten 1 ; take a large number, say 10,000, then there will be 

 about 3640 who live to over sixty, and about 3540 who do 

 not reach ten ; hence the total number who do not die within 

 the assigned limits will be about 2820 altogether. Of course 

 if these proportions were accurately assigned, the resultant 

 sum would be equally accurate : but, as the reader knows, in 

 Probability this proportion is merely the limit towards which 

 the numbers tend in the long run, not the precise result 

 assigned in any particular case. Hence we can only venture 

 to say that this is the limit towards which we tend as the 

 numbers become greater and greater. 



This rule, in its general algebraic form, would be ex 

 pressed in the language of Probability as follows: If the 

 chances of two exclusive or incompatible events be re 

 spectively and -- the chance of one or other of them 

 m n 



1 1 m -\- n 



happening will be h - or - . Similarly if there were 

 m n inn 



more than two events of the kind in question. On the prin 

 ciples adopted in this work, the rule, when thus algebraically 

 expressed, means precisely the same thing as when it is 

 expressed in the statistical form. It was shown at the con 

 clusion of the last chapter that to say, for example, that the 



chance of a given event happening in a certain way is ^ , is 



only another way of saying that in the long run it does tend 

 to happen in that way once in six times. 



It is plain that a sort of corollary to this rule might be 



1 The examples, of this kind, re- high authority of De Morgan for re 

 ferring to human mortality are taken garding them as the best representa- 

 from the Carlisle tables. These tive of the average mortality of the 

 differ considerably, as is well known, English middle classes at the present 

 from other tables, but we have the day. 



