4i 
Mr . Morgan on SurvivorJhlpu 
PROBLEM. 
Suppofing the ages of A, B, and C, to be given ; to deter- 
mine, from any table of obfervations, the value of the fum 
S payable on the contingency of C’s furviving B, provided the 
life of A (hall be then extinfh 
SOLUTION. 
.Let a reprefent the number of perfons living in the table at the 
age of A. Let a' 9 a'\ a' !t , &c. reprefent the decrements of 
life at the end of the ift, 2d, 3d, 4th, &cc. years from the age of 
A. Let b reprefent the number of perfons living at the age 
of B, and w, n , o 9 p 9 &c. the number of perfons living at the 
end of the ift, 2d, 3d, 4th, &c. years from the age of B. In 
like manner let c reprefent the number of perfons living at the 
age of C, and d 9 e, f\ g 9 &c. the number of perfons living at the 
end of the ift, 2d, 3d, 4th, &c. years from the age of C 
Let r alfo denote the value of £• 1 Increafed by its intereft for a 
year. In order to receive the fum S in the firft year, it is 
neceflary either that all the three lives (hall have died in that 
year, A having died firft, B next, and C laft ; or that only the 
two lives A and B (hall have died (A having died firft), and 
that C (hall have lived to the end of that year. The proba- 
bility that the three lives (hall die in the firft year is 
The probability that they (hall die in the order 
above mentioned is The probability that both 
6 . abc 
a' . b—m 
A and B (hall die in the firft year is ^ 
Vol. LXXIX. G 
Half this frac- 
tion. 
