SECT. 11.] 



Inverse Probability. 



181 



facts, emotions, inferences, &c., as may be properly associ 

 ated with it. 



11. Have we to interpret the second example in a 

 different way ? Here also we have a single instance, but the 

 nature of the question would seem to decide that the only 

 series to which it can properly be referred is the following I 

 Balls are continually drawn from different bags each contain 

 ing ten, and are always found to be white ; what is ultimately 

 the proportion of cases in which they will be found to have 

 been taken from bags with only one white ball in them ? 

 Now it may be readily shown 1 that time has nothing to 

 do with the question ; omitting therefore the consideration 

 of this element, we have for the two series from which our 

 opinions in these two examples respectively are to be 

 formed : (1) balls of different colours presented to us in a 

 given ultimate ratio ; (2) bags with different contents simi 

 larly presented. From these data respectively we have to 

 assign their due weight to our anticipations of (1) a white 

 ball ; (2) a bag containing but one white ball. So stated the 

 problems would appear to be formally identical. 



When, however, we begin the practical work of solving 

 them we perceive a most important distinction. In the first 

 example there is not much that is arbitrary; balls would 

 under such circumstance really come out more or less accu 

 rately in the proportion expected. Moreover, in case it 

 should be objected that it is difficult to prove that they will 

 do so, it does not seem an unfair demand to say that the balls 

 are to be well-mixed or fairly distributed/ or to introduce 

 any of the other conditions by which, under the semblance of 

 judging a priori, we take care to secure our prospect of a 



1 This point will be fully discussed 

 in a future chapter, after the general 

 stand-point of an objective system 



of logic has been explained and illus 

 trated. 



