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event has happened, my expectation ought to be 
efteemed the fame in value as before, i. e. x y 
and confequently the probability of my obtaining 
N is (by definition 5) ftill ^ or j*. But after this 
difcovery the probability of my obtaining N is the pro- 
bability that the ift of two fubfequent events has hap- 
pened upon thefuppofition that the 2d has, whofe pro- 
babilities were as before fpecified. But the probability 
that an event has happened is the fame as the proba- 
bility I have to guefs right if I guefs it has happened. 
Wherefore the following proportion is evident. 
P R O P. 5. 
If there be two fubfequent events, the probability 
of the 2d — and the probability of both together 
and it being 1 ft difcovered that the 2d event has hap- 
pened, from hence I guefs that the ift event has al- 
fo happened, the probability I am in the right is 
PROP. 
* What is here faid may perhaps be a little illuftrated by con- 
fid ering that all that can be loft by the happening of the 2d event 
is the chance I fhould have had of being reinftated in my former 
circumftances, if the event on which my expe&ation depended had 
been determined in the manner expreffed in the propofition. But 
this chance is always as much againji me as it is for me. If the 
1 ft event happens, it is againji me, and equal to the chance for 
the 2d event’s failing. If. the ift event does not happen, it is 
for me, and equal alfo to the chance for the 2d event s failing. 
The lofs of it, therefore, can be no difadvantage. 
t What is proved by Mr. Bayes in this and the preceding pro- 
pofition is the fame with the anfwer to the following queftion. 
Vv r hat is the probability that a certain event, when it happens, will 
Vol. LIII. Ddd be 
