[ no ] 



and that one will happen and the other fail. This mode of calcu- 

 lation adopted by Dr. Waring, however it may hold in joint an- 

 nuities, where the defired end is equally anfwered, whether one or 

 all of the lives attain the propofed period, will not equally apply 

 to the conjoint probability of arguments, or concurring witnefles, 

 where the evidence fails either when the arguments are all falfe, 

 or are oppofed to each other. 



If the witnefles that atteft a fad, or the voters that decide on a 

 queftion, contradid each other, and it be required to determine 

 what is the refulting probability of the truth of the fad or of the 

 decifion upon the whole, we are to proceed thus : firft compute 

 the odds that the affirmative witnefles are right, or the ratio of the 

 number of chances of their being right to the number of chances 

 of their being in errror; proceed in the fame manner with the 

 negative witneflTes ; then the produd of the number of chances 

 -that the affirmative witneflTes are right, into the number of chances 

 that the negative witnefl'es are miftaken, will be the nun.ber of 

 chances for the truth of the fad ; and the produd of the number 

 of chances that the affirmative witneflTes are miftaken, into the 

 number of chances that the negative witnefl"es are right, will be 

 the number of chances for the falfliood of the fad ; and confe- 

 quently the probabihty of the truth of the fid refulting upon 

 the whole, will be equal to the former produd divided by the 

 fum of the two produds. For example, let there be feven voters, 

 of which let four be affirmative and three negative; and let the 



chance 



