on Survi'oorjhips . ^33 
c"'\ Sec. reprefent the decrements of life at the end of the 
I ft, 2d, 3d, 4th, Sec. years from the age of A. Let b repre- 
fent the number of perfons living at the age of B the older of 
the two lives, and c, d , e,f Sec. the number of perfons living 
at the end of the ift, 2d, 3d, 4th, &c. years from the age of 
B. Suppofing now it were required to determine the probabi- 
lity of B’s furviving A in the firft year. It is manifeft that 
this event may take place either by A’s dying before the end of 
the year and B’s furviving that period, or by the extin&ion 
of both the lives, reftrained however to the contingency of B’s 
having died l aft. The probability that A dies in the firft year, 
r 
and that B furvives it, is exprefled by the fraction The 
probability that both the lives die in this year is exprefted by 
; and as it is very nearly an equal chance that 
the fraction 
a' . b — c 
A dies ff, this fraction fhould be reduced one-half and then 
a' . f—c 
it will become = 
2 ab 
Hence the whole probability of B’s 
a c a' • b — c a . b + c 
+ 
furviving A in the firft year will be = ^ 
the fame manner the probability of B’s furving A in the 2d, 
^ a" . c 4- d a ,n . d-\-e 
3d, 4th, &c. years may be found -— ~ b 
&c. refpeflively ; 
2 ab r 
furviving A will be = — L x 
0 a 0 
therefore, the whole probability of B’s 
b + c , c+d ,, a + e /// , e ±f a "" 
— a -\ a 4 -—— a + a * 
222 
See. 
Having found by the preceding feries the probability of B, 
the elder life’s, furviving A the younger ; the other expreftion, 
Y y 2 which 
