USE OF TABLES. 91 



480. But this is not the same set of circumstances as 

 that of the problem in page 77- We are there sup- 

 posed to know exactly in what proportion As and Bs are 

 contained in an urn ; and with this positive knowledge 

 we can ascertain the probability of drawing any given 

 number of As in a given number of trials. In the 

 present instance we do not know the contents of the 

 urn, but only the result of a certain number of drawings, 

 from which we can draw presumptions, as in page 53. 

 about the whole contents. The determination of chances 

 relative to a new set of trials depends upon two risks in 

 the latter case, and upon one only in the former. The 

 latter problem is therefore more complicated in its prin- 

 ciples though not so in its results. 



Let us suppose two different persons, John and 

 Thomas, thus situated with respect to the contents of an 

 urn: John knows that there are as many As as Bs; 

 Thomas has observed a hundred successive drawings, of 

 which (so let it have happened) fifty have given A, and 

 as many have given B. That which John knows is 

 rendered not improbable to Thomas by the result of 

 the trials, while the same result would have been thought 

 not unlikely beforehand by John. But there is this 

 difference between their degrees of knowledge, that John 

 has the certainty of a fact (the equality of As and Bs), 

 of which Thomas can only say that the fact, or some- 

 thing near it, is extremely probable. No one could 

 argue with John against any particular venture in such 

 a lottery upon the ground of the possibility of the As 

 much exceeding the Bs; while with Thomas it might 

 be urged as possible, though not probable, that the 

 former might exceed the latter a hundred-fold. Again, 

 suppose John and Thomas, having equal fortunes, are 

 disposed to venture as far as produce woultl warrant, 

 upon the results of a hundred (to Thomas a second 

 hundred) trials. It is obvious to common sense that 

 Thomas must not venture so much as John ; for he 

 runs a larger risk, seeing that he assumes as an average 

 result what possibly may have been a rare occurrence. 



