SECT. 5.] The Rules of Inference in Probability, 173 



One man in ten, say, has black hair, and one in twelve 

 is short-sighted ; what conclusions could we then draw as 

 to the chance of any given man having one only of these 

 two attributes, or neither, or both ? It is clearly possible 

 that the properties in question might be inconsistent with 

 one another, so as never to be found combined in the same 

 person ; or all the short-sighted might have black hair ; or 

 the properties might be allotted 1 in almost any other propor 

 tion whatever. If we are perfectly ignorant upon these 

 points, it would seem that no inferences whatever could be 

 drawn about the required chances. 



Inferences however are drawn, and practically, in most 

 cases, quite justly drawn. An escape from the apparent 

 indeterminateness of the problem, as above described, is 

 found by assuming that, not merely will one-tenth of the 

 whole number of men have black hair (for this was given as 

 one of the data), but also that one-tenth alike of those who 

 are and who are not short-sighted have black hair. Let us 

 take a batch of 1200, as a sample of the whole. Now, from 

 the data which were originally given to us, it will easily be 

 seen that in every such batch there will be on the average 

 120 who have black hair, and therefore 1080 who have not. 

 And here in strict right we ought to stop, at least until we 

 have appealed again to experience ; but we do not stop here. 

 From data which we assume, we go on to infer that of the 

 120, 10 (i.e. one-twelfth of 120) will be short-sighted, and 

 110 (the remainder) will not. Similarly we infer that of the 



1 I say, almost any proportion, be- men are short-sighted, for in any 



cause, as may easily be seen, arith- given batch of men the former are 



metic imposes certain restrictions more numerous. But the range of 



upon the assumptions that can be these restrictions is limited, and 



made. We could not, for instance, their existence is not of importance 



suppose that all the black-haired in the above discussion. 



