334 Reply to Mr. Hawes, on the Doctrine of Probabilities. [May V5 
and only 581 at the age of 50, the pro- 
bability of a person aged 20 living 30 
years, or attaining the age of 50, Is the 
ratio of the number living at this age, to 
this number and to the number who have 
died since the ave of 20; that is im the 
ratio of 581 to 5814235, or $14, and 
is therefore properly expressed by the 
a 
ames an! 
fraction ——~, and for the same reason 
614 
the probability that-a person aged 40 
shall live 30 years, is, by the same table, 
found to be ==, but the probability 
69 
both these persons shall live 50 years, is 
the product of the two probabilities or 
<i 80 : 
a ee which may be thus 
4°°657 = 55409 
na 
shewn: in is the probability of a life 
4 
of 20, continuing 30 years, and it were 
certain that a person of 40 would conti- 
nue the same time, then would the pro- 
bability of their joint continuance that 
8 : 
period be, ot 1, (which denotes cer- 
tainty) and would therefore still be 
531 
S14 ! 
that.a, person aged 40 shall live 30 years, 
; but as instead of its being certain 
yates 310 ie 
the probability is only ase? the fraction 
J 
= therefore must evidently be de- 
814 $10 
657 
we have this proportion as 
581 180110 
creased in the ratio of unity to 
whence 
» the probabi- 
lity of both lives continuing 30 years, as 
before stated. I trust all this is so evi- 
dent and so easy of comprehension, that 
no doubts of its truth can be entertained 
hy any of your readers excepting Mr, 
Hawes, from whom | have no such ex- 
pectation, because that gentleman does 
not scruple to assert that the doctrine is 
founded in fallacy, and, instead of adopt- 
ing it, he somewhat pompously tells us, 
« That by consulting nature in preference 
to his own imagination, or to any re- 
ceived doctrine, he finds” (although by 
what method he does not condescend to 
inform us) ‘the probability, from the 
same Table of Observations of a person 
‘whose age is 20, attaining the age of 50, 
ae 56639 
er living 30 years to be 300000 7°" of 
‘a person aged 40 living 80. years, 
23,4056 
30,0000 
their both continuing to live $0 years, 
24,6580 
30,0000 
-years, and the probability of 
years,” thus making the pro- 
‘bability of their both continuing to live 
80 years, to be greater than the probabi- 
lity of the latter of the 2 lives only 
continuing that term, as he has also 
done in his other case of 2 joint lives, 
as well as in the case of S joint lives. 
Now surely the absurdity of contending 
that the probability of the happening of 
two events, is greater than the probabi- 
Jity that one only of the events shall take 
place, is so great, that I trust none of 
your readers will feel disposed to have 
any faith in the deductions which this, 
writer boasts of having obtained from 
consulting of nature. 
In the following example Mr. H. again 
objects to the doctrine, on the grounds. 
of its producing absurd results, and says, 
that from the same table, ‘‘ he finds the 
probability of a life aged 20 attaining, 
40,2199 
75,0000 
life aged 30 attaining the same age 
34,0586 
—— years, and of a life aged 40 ate 
65,0000 >? a8 
the age of 95 to be years, of a 
ate 3+)''' 264802 
taining the same age FCW baad but 
, 1 
that the probability all these persons 
shall continue for the term of 55 years, is 
33,6807 
55,0000” 
as necessarily resulting from the doctrine, 
subscribed by the mathematical faithful, 
enrolled in their court of chancery.” 
Now the absurdity which Mr. H. so tri- 
usnphantly exultsin, recoils upon himself, 
for in the table which he makes use of, 
none of the persons attain a greater age 
than 94 years, yet he makes the proba= 
bility that all these lives shall continue 
55 years (that is, that.one of them shall 
attain an age greater by a yearthan any 
, 33,6807 Ko 
in the table) to be one he whilst 
instead of the nonentity 0000, 
the result by the usual method, however 
it may excite his ridicule, docs’ most 
truly represent the probability, or rather 
denotes that no such probability can exist. ° 
T can only reply to Mr. H.’s statement 
of “ the probability of a person aged 15 
continuing 10 years, beipg equal to a 
period of nine years, and the fraction 
5857,” by saying that the expression ap 
pears to me to be altogether destitute of 
meaning.  - * - B. Hooke. 
Eagle Office, April 6,.1811.-- 
For 
