168 The Rules of Inference in Probability. [CHAP. vn. 



able to deduce the rules of probability given in ordinary 

 treatises upon the science. It would be more correct to say 

 that we are able to deduce some of these rules, for, as will 

 appear on examination, they are of two very different kinds, 

 resting on entirely distinct grounds. They might be divided 

 into those which are formal, and those which are more or less 

 experimental. This may be otherwise expressed by saying 

 that, from the kind of series described in the first chapters, 

 some rules will follow necessarily by the mere application of 

 arithmetic ; whilst others either depend upon peculiar hypo 

 theses, or demand for their establishment continually re 

 newed appeals to experience, and extension by the aid of the 

 various resources of Induction. We shall confine our atten 

 tion at present principally to the former class ; the latter can 

 only be fully understood when we have considered the con 

 nection of our science with Induction. 



2. The fundamental rules of Probability strictly so 

 called, that is the formal rules, may be divided into two 

 classes, those obtained by addition or subtraction on the 

 one hand, corresponding to what are generally termed the 

 connection of exclusive or incompatible events 1 ; and those 

 obtained by multiplication or division, on the other hand, 

 corresponding to what are commonly termed dependent 

 events. We will examine these in order. 



(1) We can make inferences by simple addition. If, 

 for instance, there are two distinct properties observable in 

 various members of the series, which properties do not occur 

 in the same individual; it is plain that in any batch the 

 number that are of one kind or the other will be equal to the 

 sum of those of the two kinds separately. Thus 36.4 infants 



1 It might be more accurate to or mutually exclusive classes of 

 speak of incompatible hypotheses events , 

 with respect to any individual case , 



