Survivorjhlps. 
267 
PROBLEM VIII. 
To find the value of a given fum payable on the death 01 
A or B, fhould either of them be the firjl that fhall fail of the 
three lives A, B, and C. 
SOLUTION. 
In each year the payment of the given fum will depend upon 
either of fix events, ift. If the three lives fhould fail in the 
year, A or B having died firft. zdly, if A and B fhould die in 
the year, and A live. 3dly, If C fhould die after A in the 
year, and B live. 4thly, If C fhould die after B in the year, 
and A live. 5thly, If A only fhould die in the year, 
and B and C both live. 6thly, If B only fhould die in the 
year, and A and C both live. T he fractions denoting the fe 
_ . . . 2S , Tea' , md • a" neat" 
feveral contingencies are =3 — * 1 - — s ** — “ + occ ' 
2 S ^ beat , md 9 a! 
— — r ^ ' Hr* z - 
yibc r r 
l x ^ + ^+&c. + ix^+^ 
6 ate r r a r 3 S ai( r r 
nf . a 1 
+ &c. + 
S mda! neat 
babe ^ a 
ofa 
0 S b — m.c m- 
. + &c -+3, x — + V 
n .d 
V-T 1 + 
o.abc r 
md.a' ~ta 
77 
** + ______ 
+ 
md .a' , ne . a' + d 
labc 
+ &c. 
S into — X 
(3. FK-AFK 
2b 
+ 
bk-abk 
B . FC- AFC , a.r-i.BC-ABC^ ”-^-^ - L. x 
gj r 3 r "** 6^r 
vi . PT — APT 
2^ 
(£ denoting the value of S on. 
BT-ABT + 
the contingency of C’s furviving B, as in Prob. 40 
N n 2 
The 
