

SECT. 3.] The Rules of Inference in Probability. 171 



certain ; hence the fraction which represents the chance of 

 an event which is certain becomes unity. 



It will be equally obvious that given that the chance that 



an event will happen is , the chance that it will not happen 



1 m-1 

 is 1 or - 



in m 



3. (2) We can also make inferences by multiplication 

 or division. Suppose that the two events, instead of being 

 incompatible, are connected together in the sense that one 

 is contingent upon the occurrence of the other. Let us be 

 told that a given proportion of the members of the series 

 possess a certain property, and a given proportion again of 

 these possess another property, then the proportion of the 

 whole which possess both properties will be found by multi 

 plying together the two fractions which represent the above 

 two proportions. Of the inhabitants of London, twenty-five 

 in a thousand, say, will die in the course of the year ; we 

 suppose it to be known also that one death in five is due to 

 fever ; we should then infer that one in 200 of the inhabitants 

 will die of fever in the course of the year. It would of course 

 be equally simple, by division, to make a sort of converse 

 inference. Given the total mortality per cent, of the popula 

 tion from fever, and the proportion of fever cases to the 

 aggregate of other cases of mortality, we might have inferred, 

 by dividing one fraction by the other, what was the total 

 mortality per cent, from all causes. 



The rule as given above is variously expressed in the 

 language of Probability. Perhaps the simplest and best 

 statement is that it gives us the rule of dependent events. 



That is ; if the chance of one event is , and the chance that 



m 



if it happens another will also happen is , then the chance 





