42, Mr. Morgan on Survivorjhips, 
tion, or * s the probability that the death of A fhall 
happen before the death of B in this year. The probability 
that C fhall furvive A and B, reftrained to the contingency of 
A’s having died firft, is 
cl » b — ?n . d 
2 abc 
The value therefore of the 
S 
Z' or 1 r n • n a f . b — m . c — d a . b — m . d 
fum S for the firft year is b x z — — — + 
abc a'mc a'ab ami 
t> ~ b 3 3 
• ••••«• 
6 . abcr 1 labor abcr 
• In the fecond year the pay- 
ment of the given fum will depend on either of four events 
happening. Firft, on the contingency of all the three lives 
dying in that year, A having died firft, B next, and C laft. 
2dly, On the contingency of B’s dying in that year, C’s living 
to the end of it, and A’s dying in the firft year, ^dly, On 
the contingency of B’s dying after A in the fecond year (both 
of them having furvived the firft year) and of C’s living to the 
tend of that year. 4thly, On the contingency of A’s dying in 
the firft year, and of B and C’s both dying in the fecond year, 
B having died firft. The probability of the firft contingency 
Is expreffed by the fraction — ■ The probability of 
the fecond by the fraction 
third by the fraction ~- m - 
J 2 . abc 
a . m — n . e 
abc 
The probability of the 
m — n . e 
fourth contingency by the fraction 
And the probability of the 
Thefe feve- 
a ' . m— n . d—e 
2 abc 
xal fractions, therefore, multiplied into ~ will be the value of 
:the given fum for the fecond year, and may be eafily founds 
In like 
■~<abcc 
S a" dm a /f dn a" cm a"en a'em a! en a' dm 
X — — 7- - — 4— 
- 6 ^ 3 “ 3 2 2 2 
6 
a' dn 
2 
manner 
