ON THE DOCTRINES OF CHANCE. JgOJ 



truth of the elementary doctrines of chance," shovild you 

 think the following remarks upon the subject likely to re- 

 move the doubts of your correspondent, you will, by their 

 insertion, oblige 



Your very humble Servant, 



W. SAINT. 



Opsimath begins by quoting what he deems to be the Sense of the 

 sense of the first case of de Moivre in these words, " Any Moivref ^"^ 

 *' one undertaking with a die of six sides, to cast an ace in one 

 *' throvvjhas \ of the six possible chances in his favour, and the 

 *' remaining ^ against him ; tlie whole six chances Icing cer~ 

 " tainty or at least such in the event ofcontimced trials.''^ Now 

 this latter clause of the supposed quotation (I say supposed pj^j. sense ir-w. 

 quotation, for Opsimath confesses, that he had not a copy of i^ken. 

 the work at hand), is not to be found in the first case of de 

 Moivre, or yet in any other case ; neither can it be inferred 

 from anything which he has said on the subject throughout 

 the whole of his work. Indeed had Opsimath proceeded 

 but a few pages farther than the first case, he would have 

 seen, that it was impossible for de Moivre to have considered 

 this as an elementary doctrine of chance, for at Art. 11 he 

 says, <' Let a be the number of chances for the happening The actual 

 " of an event, and b the number of chances for its failing, ^^ctrine oi d.- 

 *' then the probability of its happening once in any number of 

 a a b ab^ 



" frialswill bp — --- + ^ 4- &c., till the 



«+ o l^+b\ ^t^T\^ 

 *' number of terms be equal to the number of trials given:" 

 the application of which would give ^^ff^ for the probabi- 

 lity of throwing an ace once in six throws; whereas Opsi- 

 math infers, and infers justly, from the expression which he 

 attributes to de Moivre, that f or certainty would be the 

 amount of the probability; and this single circumstance, 

 had Opsimath proceeded so far, would have convinced hiin, 

 that he must either have attributed that to de Moivre which 

 he had never asserted, or else, at least, that he himself 

 must have misunderstood him. 



Since the clause abovementioned appears to have been 

 the foundation of Opsimath's scruples, and since this clause 



