OF THE CALCULATION OF CHANCES. 63 



that it will not. But its probability to us means the degree 

 of expectation of its occurrence, which we are warranted in 

 entertaining by our present evidence. 



Bearing this in mind, I think it must be admitted, that 

 even when we have no knowledge whatever to guide our 

 expectations, except the knowledge that what happens must 

 be some one of a certain number of possibilities, we may still 

 reasonably judge, that one supposition is more probable to us 

 than another supposition ; and if we have any interest at 

 stake, we shall best provide for it by acting conformably to 

 that judgment. 



2. Suppose that we are required to take a ball from a 

 box, of which we only know that it contains balls both black 

 and white, and none of any other colour. We know that the 

 ball we select will be either a black or a white ball ; but we 

 have no ground for expecting black rather than white, or 

 white rather than black. In that case, if we are obliged to 

 make a choice, and to stake something on one or the other 

 supposition, it will, as a question of prudence, be perfectly 

 indifferent which ; and we shall act precisely as we should 

 have acted if we had known beforehand that the box contained 

 an equal number of black and white balls. But though 

 our conduct would be the same, it would not be founded on 

 any surmise that the balls were in fact thus equally divided ; 

 for we might, on the contrary, know, by authentic informa- 

 tion, that the box contained ninety-nine balls of one colour, 

 and only one of the other ; still, if we are not told which 

 colour has only one, and which has ninety-nine, the drawing 

 of a white and of a black ball will be equally probable to us ; 

 we shall have no reason for staking anything on the one event 

 rather than on the other ; the option between the two will 

 be a matter of indifference ; in other words it will be an even 

 chance. 



But let it now be supposed that instead of two there are 

 three colours white, black, and red ; and that we are entirely 

 ignorant of the proportion in which they are mingled. We 

 should then have no reason for expecting one more than 



