376 BISHOP TERROT ON PROBABILITIES. 
But when the given probabilities are of different events, and the queesitum is 
the probability of their joint occurrence, the ratio alone is sufficient, because as 
factors“? and “” give the same results. 
mq 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 3 =. (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 @ priori probability derived from absolute ignorance has no effect 
upon the force of a subsequently admitted probability. (11, 12.) 
