[ 88 ] 



'Ira perfon therefore tells me, that an event has happened, Tjy 

 v/hich I am to receive a fum of money, my expedtatioa of re- 

 ceiving that fum has a determinate value, before I certainly know 

 ■whether that event has adlually happened or not. 



In all cafes, the expedlation of obtaining any fum is eftimated 

 by multiplying the value of the fum expecSled by the fradlion 

 which reprefents the probability of obtaining it. Thus if my 

 probability of obtaining ;^ioo be j-, my expectation will be 

 = 1x^100 = ^60. 



Therefore it neceflarlly follows, that the probability of ob- 

 taining the fum is equal to the value of the expe(5lation, divided 

 by the value of the thing expedled. And fince the expedlation 

 is neceflarily determinate, fo likewife is the probability. Now 

 my expeclation, derived from the report of the witncfs, muft be 

 either equal to, greater, or lefs than the expsAation derived 

 from an equal chance ; the probability will therefore be either 

 equal to, greater, or lefs than an equal chance ; therefore the 

 probability in the former cafe is homogeneous with the proba- 

 bility in the latter ; but the latter is capable of being exprefled 

 fradlionally, therefore fo alfo is the former. 



Suppose a perfon of good charadler tells me, that an event 

 has happened by which i am to receive j^ioo; there will hence 

 arife an expedlation in my mind, which muft be of fome de- 

 terminate 



