[ 3io ] 
which ever of thefe ways I guefs, my chance 
is £ exaCtly. This may be proved in the fame 
manner with the foregoing cafes, where q is greater 
than />, or may be proved from them by confidering 
the happening and failing of an event, as the fame 
with the failing and happening of its contrary. 
4thly, Other things fuppofed the fame, whether q 
be greater or lefs than />, and I judge that the proba- 
f) P 
bility of the event lies between — -\- z and z, 
my chance is greater than — — - , and 
* I+2E/* ? + 2E«V 
n 
lefs than This is an evi- 
I — 2 E a b q — 2E a b 
n 
dent corollary from the cafes already determined. 
And here, if p — y, my chance is 2 £ exa&ly. 
Thus far I have tranfcribed Mr. Bayes. 
It appears, from the Appendix to the Eflay, that 
the rule here demon ft rated, though of great ule, 
does not give the required chance within limits fuf- 
ficiently narrow. It is therefore neceftary to look out 
for a contraction of thefe limits; and this, I think, 
we fhall difcover by the help of the following de- 
ductions ; which, for the fake of greater dinftinCtnefs, 
1 fhall give as a continuation of the foregoing Ar- 
ticles. 
13. The 
