[ 3^0 j 
pending on the failure of the 2d event the probability 
of which (by cor. prop. 1) is ' or -, becaufe y is 
to x as N — b to N. Wherefore fince x is the thing 
expeCted and - the probability of obtaining it, the 
value of this expectation is^y. But thefe two lad; ex- 
pectations together are evidently the fame with my 
original expectation, the value of which is x, and 
therefore P -\-y — at. But y is to x as N — b is to N. 
Wherefore x is to P as N is to b, and — (the 
. P 1 
probability of my obtaining N) is -• 
Cor. Suppofe after the expectation given me in the 
foregoing propofition, and before it is at all known 
whether the ift event has happened or not, I fhould 
find that the 2d event has happened ; from hence I 
can only infer that the event is determined on which 
my expectation depended, and have no reafon to 
efteem the value of my expectation either greater or 
lefs than it was before. For if I have reafon to think 
it lefs, it would be reafonable for me to give fomething 
to be reinftated in my former circumftances, and 
this over and over again as often as I fhould be in- 
formed that the 2d event had happened, which is evi- 
dently abfurd. And the like abfurdity plainly follows 
if you fay I ought to fet a greater value on my expec- 
tation than before, for then it would be reafonable for 
me to refufe fomething if offered me upon condition 
I would relinquifh it, and be reinftated in my former 
circumftances and this likewife over and over again 
as often as (nothing being known concerning the ift 
event) it fhould appear that the 2d had happened. 
Notwithftanding therefore this difcovery that the 2d 
event 
