[ 4-00 ] 
an inveftigation which it would be too tedious to give 
here, has deduced from this rule another, which is as 
follows. 
RULE 2. 
If nothing is known concerning an event but that 
it has happened p times and failed q in p -j- q or n 
trials, and from hence I guefs that the probability of 
its happening in a fingle trial lies between - +2 and 
- — % i if —— a — b — f, E the coefficient 
n p q n n 
of the term in which occurs af b* when a -|- /£)"■- is 
expanded, and ^ X x E J b q x 
n V n 
np z 3 
by the feries mz — 
3 * 1 * * * 2« 
, m 7 z 7 . n-2 n-A. n- 6 m 9 z 9 
+ TTX-X — x — 
. n—2 ^ nf z 5 * »— 2 X n— 4 
1 o» 5 
2 n X yi 
See. 
my chance to be in the right is greater than 
2 v 
i + 2 E af b? -|- 2 E af b? * and lefs than 
2JB n 
1-2 E apbi — 2 E af b*. And i i p q my chance 
n 
is 2 £ exa&ly. 
* In Mr. Bayes’s manufeript this chance is made to be gieater 
2X 2S 
than — ; — — 7-— and lefs than — — jr— . The third term 
1 + 2 aP bl 1 — 2 h af b* 
in the two divifors, as I have given them, being omitted. But 
this being evidently owing to a fmall overfight in the dedu&ioN 
of this rule, which I have reafon to think Mr. Bayes had himfelf 
difeovered, I have ventured to correct his copy, and to give the 
rule as 1 am fatisfied it ought to be given, 
In 
