^46 OF THE THEORY OF PROBABILITIES. [CHAP. XVI. 



connected event, or combination of events, constitutes the cor- 

 responding quasitum, or object sought. Now in the most gene- 

 ral, yet strict meaning of the term "event," every combination 

 of events constitutes also an event. The simultaneous occur- 

 rence of two or more events, or the occurrence of an event under 

 given conditions, or in any conceivable connexion with other 

 events, is still an event. Using the term in this liberty of appli- 

 cation, the object of the theory of probabilities might be thus 

 denned. Given the probabilities of any events, of whatever 

 kind, to find the probability of some other event connected with 

 them. 



5. Events may be distinguished as simple or compound, the 

 latter term being applied to such events as consist in a combina- 

 tion of simple events (I. 13). In this manner we might define it 

 as the practical end of the theory under consideration to deter- 

 mine the probability of some event, simple or compound, from 

 the given probabilities of other events, simple or compound, 

 with which, by the terms of its definition, it stands connected. 



Thus if it is known from the constitution of a die that there 



is a probability, measured by the fraction ^, that the result of 



any particular throw will be an ace, and if it is required to deter- 

 mine the probability that there shall occur one ace, and only one, 

 in two successive throws, we may state the problem in the order 

 of its data and its qucesitum, as follows : 



FIRST DATUM. Probability of the event that the first throw 



11 l 



will give an ace = -. 



SECOND DATUM. Probability of the event that the second 

 throw will give an ace = ^. 



QU^SITUM. Probability of the event that either the first 

 throw will give an ace, and the second not an ace ; or the first 

 will not give an ace, and the second will give one. 



Here the two data are the probabilities of simple events de- 

 fined as the first throw giving an ace, and the second throw 

 giving an ace. The quaesitum is the probability of a compound 

 event, a certain disjunctive combination of the simple events 



