C 379 ] 
fame ratio of P to N is compounded of the ratio of 
a to N and that of b to N, i. e. the probability that 
the two fubfequent events will both happen is com- 
pounded of the probability of the ift and the proba- 
bility of the 2d on fuppofition the ift happens. 
Corollary. Hence if of two fubfequent events the 
probability of the ift be and the probability of 
P ^ 
both together be — , then the probability of the 2d 
N # p 
on fuppofition the 1 ft happens is -. 
PROP. 4. 
If there be two fubfequent events to be determined 
every day, and each day the probability of the 2d is 
^ and the probability of both ^ , and I am to re- 
ceive N if both the events happen the ift day on 
which the 2d does; I fay, according to thefe con- 
p 
ditions, the probability of my obtaining N is For 
if not, let the probability of my obtaining N be ~ 
and let be to x as N — b to N. Then fince — is the 
probability of my obtaining N (by definition 1) x is 
the value of my expectation. And again, becaufe ac- 
cording to the foregoing conditions the ift day I have 
an expectation of obtaining N depending on the hap- 
pening of both the events together, the probability of 
which is — , the value of this expectation is P. Like- 
wife, if this coincident fliould not happen I have an 
expectation of being reinflated in my former circum- 
ftances, i, e. of receiving that which in value is x de- 
pending 
