CHAP. XVI.] OF THE THEORY OF PROBABILITIES. 247 



involved or implied in the data. Probably it will generally hapr- 

 pen, when the numerical conditions of a problem are capable of 

 being deduced, as above, from the constitution of things under 

 which they exist, that the data will be the probabilities of simple 

 events, and the qusesitum the probability of a compound event 

 dependent upon the said simple events. Such is the case with a 

 class of problems which has occupied perhaps an undue share of 

 the attention of those who have studied the theory of probabilities, 

 viz., games of chance and skill, in the former of which some 

 physical circumstance, as the constitution of a die, determines 

 the probability of each possible step of the game, its issue being 

 some definite combination of those steps ; while in the latter, the 

 relative dexterity of the players, supposed to be known a priori, 

 equally determines the same element. But where, as in statisti- 

 cal problems, the elements of'our knowledge are drawn, not from 

 the study of the constitution of things, but from the registered 

 observations of Nature or of human society, there is no reason 

 why the data which such observations afford should be the pro- 

 babilities of simple events. On the contrary, the occurrence of 

 events or conditions in marked combinations (indicative of some 

 secret connexion of a causal character) suggests to us the pro- 

 priety of making such concurrences, profitable for future instruc- 

 tion by a numerical record of their frequency. Now the data 

 which observations of this kind afford are the probabilities of 

 compound events. The solution, by some general method, of 

 problems in which such data are involved, is thus not only essen- 

 tial to the perfect development of the theory of probabilities, but 

 also a perhaps necessary condition of its application to a large 

 and practically important class of inquiries. 



6. Before we proceed to estimate to what extent known me- 

 thods may be applied to the solution of problems such as the 

 above, it will be advantageous to notice, that there is another 

 form under which all questions in the theory of probabilities may 

 be viewed ; and this form consists in substituting for events the 

 propositions which assert that those events have occurred, or 

 will occur ; and viewing the element of numerical probability as 

 having reference to the truth of those propositions, not to the oc- 



