170 The Rules of Inference in Probability. [CHAP. vu. 



obtained, in precisely the same way, by subtraction instead of 

 addition. Stated generally it would be as follows : If the 



chance of one or other of two incompatible events be and 



772* 



the chance of one alone be -, the chance of the remaining 



. n , 1 1 n m 



one will be or 



m n nm 



For example, if the chance of any one dying in a year is 

 IJT , and his chance of dying of some particular disease is ^-^ , 



9 

 his chance of dying of any other disease is - - . 



The reader will remark here that there are two apparently 

 different modes of stating this rule, according as we speak 

 of one or other of two or more events happening/ or of the 

 same event happening in one or other of two or more ways. 

 But no confusion need arise on this ground ; either way of 

 speaking is legitimate, the difference being merely verbal, 

 and depending (as was shown in the first chapter, 8) upon 

 whether the distinctions between the ways are or are not 

 too deep and numerous to entitle the event to be conven 

 tionally regarded as the same. 



We may also here point out the justification for the com 

 mon doctrine that certainty is represented by unity, just as 

 any given degree of probability is represented by its appro 

 priate fraction. If the statement that an event happens once 

 in m times, is equivalently expressed by saying that its chance 



is , it follows that to say that it happens m times in m 

 times, or every time without exception, is equivalent to 



nyi 



saying that its chance is or 1. Now an event that happens 

 every time is of course one of whose occurrence we are 



