C 4i5 ] 
that the proportion of blanks to prizes in the lottery 
was fomewhere between 9 to 1 and 11 to i, the 
chance for his being right would be .2506 &c. Let 
now enquire what this chance would be in fome 
higher cates. 
Let it be fuppofed that blanks have been drawm 
1000 times, and prizes 100 times in 1100 trials. 
In this cafe the powers of X and x rife fo high, 
, P 1 
and the number of terms in the two feriefes X 
— qX 
p + i 
6cc, and x 
P+ 1 
x 
p+ 2 
p + i 
&c. become 
p + 2 p + 1 p-\- 2 
fo numerous that it would require immenfe labour 
to obtain the anfwer by the firft rule. ’Tis neceifary, 
therefore, to have recourfe to the fecond rule. But 
in order to make ufe of it, the interval between X 
and x muft be a little altered. 44. - _ 9 _. is _i._, and 
therefore the interval berween 44 — _ * o and 44 
-}- --fo- will be nearly the fame with the interval be- 
tween _ 9 _ and 44., only fome what larger. If then 
we make the question to be j what chance there 
would be (luppoling no more known than that blanks 
have been drawn 1000 times and prizes 100 times 
in 1100 trials) that the probability of drawing a 
blank in a lingle trial would lie fomewhere between 
-14 - -4-0 an ^ -44- + -4-5- we 4 hall have a queftion 
of the fame kind with the preceding queftions, and 
deviate but little from the limits affigned in them. 
The anfwer, according to the fecond rule, is that 
2 s 
this chance is greater than 1 - 2 Ea? bi 2 E at b* 
and 
Hhh 2 
n 
