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any where between f and f, the probability that the 
event M happens p times and fails q in p-fq tri- 
als can’t be greater than the ratio of eh to A B. 
There then being thefe two fubfequent events, the 
iff that the point o will lie between e and f the 
2d that the event M will happen p times and fail q 
in p q trials, and the probability of the iff (by 
lemma i ft ) is the ratio cf ef to AB, and upon fup- 
pofition the iff happens, by what has been now 
proved, the probability of the 2d cannot be greater 
than the ratio of eh to A B, it evidently follows (from 
Prop. 3.) that the probability both together will hap- 
pen cannot be greater than the ratio compounded of 
that of ef to A B and that of eh to A B, which 
compound ratio is the ratio of fh to C A. Where- 
fore, the probability that the point 0 will lie between 
f and <?, and the event M happen p times and fail 
y, is not greater than the ratio of J h to C A. And 
in like, manner the probability the point 0 will lie be- 
tween e and d, and the event M happen and fail as 
before, cannot be greater than the ratio of e i to C A. 
And again, the probability the point 0 will lie between 
d and c, and the event M happen and fail as before, 
cannot be greater than the ratio of c i to C A. And 
laftly, the probability that the point 0 will lie between 
c * nd b, and the event M happen and fail as before, 
cannot be greater than the ratio of b k to C A. Add 
now all thefe feveral probabilities together, and their 
fum (by Prop. 1. ) will be the probability that the point 
will lie lomewhere between f and b, and the event 
M happen p times and fail q in p -j- q trials. Add 
likewise the correfpondent ratios together, and their 
fum will be the ratio of the fum of the antecedents 
to 
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