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between the two feries. Compare this with prop. 10. 
and we fhall have the following practical rule. 
RULE i. 
If nothing is known concerning an event but that 
it has happened p times and failed q in p-\-q or n trials, 
and from hence I guefs that the probability of its 
happening in a fingie trial lies fome where between 
any two degrees of probability as X and x, the 
chance I am in the right in my guefs is H-f i 
X E x' 4 into the difference between the feries X^ + I 
P+2 p +3 
— q x + q x g - 1 x x 
P + 2 
p+i 
feries x 
p+i 
&c. and the 
2 p+$ 
p+2 p+ 3 
qx + qxq-+_xx_ ~ &c. E 
P+I p + 2 2 p + 3 
being the coefficient of a p b q when a\-\-b\ n is expanded. 
This is the proper rule to be ufed when q is a fmall 
number ; but if q is large and p fmall, change every 
where in the feries here fet down p into q and ^q into p 
and ^ into r or and X into R — i-Xj which 
will not make any alteration in the difference between 
the two feriefes. 
Thus far Mr. Bayes’s effay. 
With refpett to the rule here given, it is further 
to be obferved, that when both p and q are very large 
numbers, it will not be poffible to apply it to practice 
on account of the multitude of terms which the fe- 
riefes in it will contain. Mr. Bayes, therefore, by 
F f f 2 an 
