[ I09 ] 



let be ^ and -^j then will the probability in fupport of the 

 a a 



fad, refulting from both arguments (or witneffes) be i — 

 ?2A iJ-: for if the probabilities in fupport of it are rc- 



fpedtively-r and i-, then will the refpedive probabilities of its 

 a a 



failing be i — ^~ — -^^, and i — i^ = i ; and confequcntly 



a a . a a 



the probability of failing from both will be — £j^ ^^ ; whence 



the. probability of the fad refulting from both will be r — 



a — p a — a 

 — - X 



a a 



In this argument there is one ftep, which appears inadmifllblc ; 

 it is affumed, that if the probability of failing from both, or rather 



of both failing, be = ^^x ^ ^^ ^^en i — 3^x ^ ^ =r the pro- 



a a a a 



bability of happening from both, which does not appear to be 



true; becaufe i -x — -- is equal to the probability of both 



a a 



happening, together with the probability of one happening and the 

 other failing. Thus if there be an even chance for both, 



? = - — "' — = 4 : then i = the probability that both will 



a a 1 



fail ; alfo i = the probability that both will happen, and \ — the 

 probability that one will happen and the other fail ; therefore 

 X'—\=. ^ -|- 1 = the fum of the probabilities that both will happen, 



and 



