[ 323 ]' 
P and q are taken larger, or their ratio comes 
nearer to that of equality, ’till at laid, when p and <j 
are either very great or equal, coincides with 
this mean. Thus, if either p or q is not lefs than 
30 ; that is, in all cafes, where it is not practicable 
without great difficulty to find the required chance 
exaCtly by the firft rule, Q J will be greater than the 
fourth, and lefs than the fifth of feven arithmetical 
means between C f and Ft. 
27. The arithmetical means mentioned in the lafi: 
Article may be conceived as ordinates defcribing areas 
at the fame time with Qjf ; and what has been 
proved concerning them is true alfo of the areas 
defcribed by them compared with R b i Q. 
28. If either p or q is greater than 1, the true chance 
that the probability of an unknown event which has 
happened p times and failed q in p + q or n trials, 
fibould lie fomewhere between — 4 - z and ~ 
n 1 71 
— z is lefs than 2 X, and greater than X - 4 - 
XX 1 — 2 E a b l — 2 Fab' 
— . If either p or q is 
I 1? P 1 % i TT ^ l3 
1 — E ci b — j - E ci b 
greater than 10, this chance is lefs than 2 X, and 
X X 1 — 2 E a b q — 2 E a b 
Pii 
greater than X 
1 4- 4. E + E a r b 
a n 
This 
T t 2 
