376 BISHOP TERROT ON PROBABILITIES. 



But when the given probabilities are of different events, and the qusesitum is 

 the probability of their joint occurrence, the ratio alone is sufficient, because as 



factors — and — give the same results. 



m q nq ° 



(13.) To sum up the propositions proved in the foregoing paper: — 



1. If the ratio only of equally probable cases, in two or more probabilities for 

 the same event be given, no definite probability can be derived from their compo- 

 sition. (7.) 



2. If the two given probabilities -, -, indicate not merely the ratio, but also 

 the actual number of favourable and unfavourable hypotheses or cases, their con- 

 joined force is properly expressed by £i£. (6.) 



3. Under both of these conditions, the second given probability increases or 

 diminishes the force of the first, according as the fraction expressing the second 

 is greater or less than that expressing the first. When the ratios only are given, 

 then the extent of increase or diminution is indefinite. When the actual numbers 

 are given, it is definite. (9.) 



4. The a priori probability derived from absolute ignorance has no effect 

 upon the force of a subsequently admitted probability. (11, 12.) 



