[ 403 ] 
?+3 
I 2.m x z 1 % -j- 4 
n 
3*5 
n 
n + 2 » + 4 x* + 6x8^z 5 « + 2 a « +4 x«+ 6x^+8xi6zW 
- &c. continued to any number of terms, accord- 
ing as the laft term has a poiitive or a negative fign 
before it. ° 
From fubftituting thefe values of E a f b i and m z 
z 3 n — 2 m s z 5 
— ^ r X — j- &c. in the 2d rule arifes a 
3d rule, which is the rule to be ufed when mz is of 
fome confiderable magnitude. 
RULE 3. 
If nothing is known of an event but that it has 
happened p times and failed q in p q or n trials, 
and from hence I judge that the probability of it’s 
happening in a fingle trial lies between - z and ■ 
p 
“ — % my chance to be right is greater than 
V K /> y X & v o TT Vr w »4- I w I 
multiplied by the 3 terms 2 H — x 
Vk 
Vk »-J- 2 : 
m\ K, b 
and H ftand for the quantities already explained. 
An 
