256 GENERAL METHOD IN PROBABILITIES. [CHAP. XVII. 



4. Now if this distinction of events, as simple or compound, is 

 not founded in their real nature, but rests upon the accidents of 

 language, it cannot affect the question of their mutual depend- 

 ence or independence. If my knowledge of two simple events is 

 confined to this particular fact, viz., that the probability of the 

 occurrence of one of them is /?, and that of the other q ; then I re- 

 gard the events as independent, and thereupon affirm that the 

 probability of their joint occurrence is pq. But the ground of 

 this affirmation is not that the events are simple ones, but that 

 the data afford no information whatever concerning any connexion 

 or dependence between them. When the probabilities of events 

 are given, but all information respecting their dependence with- 

 held, the mind regards them as independent. And this mode of 

 thought is equally correct whether the events, judged According 

 to actual expression, are simple or compound, i. e., whether each 

 of them is expressed by a single verb or by a combination of 

 verbs. 



o. Let it, however, be supposed that, together with the pro- 

 babilities of certain events, we possess some definite information 

 respecting their possible combinations. For example, let it be 

 known that certain combinations are excluded from happening, 

 and therefore that the remaining combinations alone are possible. 

 Then still is the same general principle applicable. The mode 

 in which we avail ourselves of this information in the calculation 

 of the probability of^any conceivable issue of events depends not 

 upon the nature of the events whose probabilities and whose 

 limits of possible connexion are given. It matters not whether 

 they are simple or compound. It is indifferent from what source, 

 or by what methods, the knowledge of their probabilities and of 

 their connecting relations has been derived. We must regard 

 the events as independent of any connexion beside that of which 

 we have infonnation, deeming it of no consequence whether such in- 

 formation has been explicitly conveyed to us in the data, or thence 

 deduced by logical inference. And this leads us to the statement 

 of the general principle in question, viz. : 



VI. The events whose probabilities are given are to be re- 

 garded as independent of any connexion but such as is either 

 expressed, or necessarily implied, in the data ; and the mode in 



