186 Inverse Probability. [CHAP. VIL 



die per thousand each year. Suppose it also known that of 

 every 100 deaths there are about 4 attributable to bronchitis. 

 The odds therefore against any unknown person dying of 

 bronchitis in a given year are 1249 to 1. Exactly the same 

 statistics are available to solve the inverse problem : A man 

 is dead, what is the chance that he died of bronchitis ? Here, 

 since the man s death is taken for granted, we do not require 

 to know the general average mortality. All that we want is 

 the proportional mortality from the disease in question as 

 given above. If Probability dealt only with inferences 

 founded in this way upon actual statistics, and these toler 

 ably extensive, it is scarcely likely that any distinction such 

 as this between direct and inverse problems would ever have 

 been drawn. 



16. Considered therefore as a contribution to the theory 

 of the subject, the distinction between Direct and Inverse Pro 

 bability must be abandoned. When the appropriate statis 

 tics are at hand the two classes of problems become identical 

 in method of treatment, and when they are not we have no 

 more right to extract a solution in one case than in the other. 

 The discussion however may serve to direct renewed atten 

 tion to another and far more important distinction. It will 

 remind us that there is one class of examples to which the 

 calculus of Probability is rightfully applied, because statistical 

 data are all we have to judge by; whereas there are other 

 examples in regard to which, if we will insist upon making 

 use of these rules, we may either be deliberately abandoning 

 the opportunity of getting far more trustworthy information 

 by other means, or we may be obtaining solutions about 

 matters on which the human intellect has no right to any 

 definite quantitative opinion. 



17. The nearest approach to any practical justification 

 of such judgments that I remember to have seen is afforded 



