ON TOE DOCTRlNiS OF CIIA-NC£. 'i5|i(|jr 



jfcthcr with that of its failing, makes certainty, which is re- 

 presented by unity, or 1, therefore the probability, that there 

 will be an ace in oncer two throws, together with the proba- 

 bility that there will not be one, is equal to unity. Now the 

 probability, that there will not be an ace the fust throw is =J-, 

 and since, whether there be one or not, the second throw will 

 be equally necessary for detennimng the probability that there 

 will not be one in tithcr throxv, therefore this second throw 

 exists with " the full force and virtue of the first, from which 

 no circumstance can deduct," viz. the probability in the se- 

 cond throw will be ^, therefore the probability that there will 

 twt be an ace in either the first or second throw will be f-Xf 

 r:^^, and, deducting this from unity, there will remain ^i- for 

 the probability that there XL-ill be an ace in either the first or 

 second throw, the same as before. 



Perhaps there is no branch of the mathematics, which is Law^ofcl^anoe 

 founded upon fewer first principles than the Laws of Cha!ice; founded on 



1 1.11 • 1 • 1 /- • • 1 r *'6''y *e^^ P""™- 



und yet probably there is no subject, the first principles or cipies yetveir 



whicli are so likely to be misapplied, or misunderstood. One ^'^^le to be 



- , . . , ^ , . . misundersloodj 



of the principal causes otthe errours in our reasoning on this 



subject, it may safely be afiirmed, is the not duly discriminat- chiefly from')M>t 

 ing between events which are dependent and those which aie b|^t^,veeiTd'^"'^ 

 independent; and this seems to have been the source, whence peiulem anc? 

 the scruples ofOpsimath have originated; scruples, which, it eveas. 

 may be asserted, have been entertained by almost every one on 

 his first entrance on this subject. Perhaps, however, what 

 has been said above may tend to remove these doubts, if not, 

 we will conclude by advising Opsimath to acquire correct 

 ideas of the first principles of ijie Laws of Chance; and if 

 in his inquiries he be guided by right reasoning, we will assure 

 liim, that there is no subject in which he will find the conclu- 

 sions more just, iiatural, or beautiful. 



As it often happens, that theory is best underslood by prac- Curnms qr,«i 

 tice, and precept best illustrated by example, I have enclosed !^'"" eluci.iij- 

 the following question, taken from the Mathematical Reposi- trmes of 

 tory, which, as it is rather of a curious nature, you may per- chance, 

 haps deem worthy of insertion; and as the solution, which I 

 have given to it, is founded upon the first and most obvious, 

 principles of the Laws of Chance, it may probably be useful 



Hot 



