184 Inverse Probability. [CHAP. vn. 



equally likely, in the other every distinct way of getting 

 each result. 



14. Uncertainties of this kind are peculiarly likely to 

 arise in these inverse probabilities, because when we are 

 merely given an effect and told to look out for the chance of 

 some assigned cause, we are often given no clue as to the rela 

 tive prevalence of these causes, but are left to determine them 

 on general principles. Give us either their actual prevalence 

 in statistics, or the conditions by which such prevalence is 

 brought about, and we know what to do ; but without the 

 help of such data we are reduced to guessing. In the above 

 example, if we had been told how the bag had been originally 

 filled, that is by what process, or under what circumstances, 

 we should have known what to do. If it had been filled at 

 random from a box containing equal numbers of black and 

 white balls, the supposition in Mr Whitworth s example is 

 the most reasonable ; but in the absence of any such infor 

 mation as this we are entirely in the dark, and the supposi 

 tion made in 12 is neither more nor less trustworthy and 

 reasonable than many others, though it doubtless possesses 

 the merit of superior simplicity 1 . If the reader will recur to 

 Ch. v. 4, 5, he will find this particular difficulty fully 

 explained. Everybody practically admits that a certain 

 characteristic arrangement or distribution has to be intro 

 duced at some prior stage ; and that, as soon as this stage 

 has been selected, there are no further theoretic difficulties 

 to be encountered. But when we come to decide, in examples 

 of the class in question, at what stage it is most reasonable 



1 Opinions differ about the defence doubtful, call it the most impartial 



of such suppositions, as they do about hypothesis. Others regard it as a 



the nature of them. Some writers, sort of mean hypothesis, 

 admitting the above assumption to be 



