OF THE CALCULATION OF CHANCES. 



3Sl 



Indecision, it is impossible for ua to 

 pronounce with certainty on their 

 occurrence. It is, however, probable 

 that any one of these events, selected 

 at pleasure, will not take place ; be- 

 cause we perceive several cases, all 

 equally possible, which exclude its 

 occurrence, and only one which fav- 

 ours it. 



** The theory of chances consists in 

 reducing all events of the same kind 

 to a certain number of cases equally 

 possible, that is, such that we are 

 equally undecided as to their exist- 

 ence ; and in determining the number 

 of these cases which are favourable 

 to the event of which the probability 

 is sought. The ratio of that number 

 to the number of all the possible cases 

 is the measure of the probability ; 

 which is thus a fraction, having for 

 its numerator the number of cases 

 favourable to the event, and for its 

 denominator the number of all the 

 cases which are possible." 



To a calculation of chances, then, 

 according to Laplace, two things are 

 necessary : we must know that of 

 sevei;3.1 events some one will certainly 

 happen, and no more than one ; and 

 we must not know, nor have any 

 reason to expect, that it will be one 

 of these events rather than another. 

 It has been contended that these are 

 not the only requisites, and that La- 

 place has overlooked, in the general 

 theoretical statement, a necessary part 

 of the foundation of the doctrine of 

 chances. To be able (it has been 

 said) to pronounce two events equally 

 probable, it is not enough that we 

 should know that one or the other 

 must happen, and should have no 

 grounds for conjecturing which. Ex- 

 perience must have shown that the 

 two events are of equally frequent 

 occurrence. Why, in tossing up a 

 halfpenny, do we reckon it equally 

 probable that we shall throw cross 

 or pile? Because we know that in 

 any great number of throws, cross 

 and pile are thrown about equally 

 often ; and that the more throws we 

 make, the more nearly the equality is 



perfect. We may know this if we 

 please by actual experiment ; or by 

 the daily experience which life affords 

 of events of the same general char- 

 acter ; or deductively, from the effect 

 of mechanical laws on a symmetrical 

 body acted upon by forces varying 

 indefinitely in quantity and direction. 

 We may know it, in short, either by 

 specific experience, or on the evidence 

 of our general knowledge of nature. 

 But, in one wa}' or the other, we 

 must know it, to justify us in calling 

 the two events equally probable ; and 

 if we knew it not, we should proceed 

 as much at haphazard in staking 

 equal sums on the result as in laying 

 odds. 



This view of the subject was taken 

 in the first edition of the present 

 work ; but I have since become con- 

 vinced that the theory of chances, as 

 conceived by Laplace and by mathe- 

 maticians generally, has not the funda- 

 mental fallacy which I had ascribed 

 to it. 



We must remember that the proba- 

 bility of an event is not a quality of 

 the event itself, but a mere name for 

 the degree of ground which we, or 

 some one else, have for expecting it. 

 The probability of an event to one 

 person is a different thing from the 

 probability of the same event to an- 

 other, or to the same person after 

 he has acquired additional evidence. 

 The probability to me that an indi- 

 vidual of whom I know nothing but 

 his name will die within the year, is 

 totally altered by my being told, the 

 next minute, that he is in the last 

 stage of a consumption. Yet this 

 makes no difference in the event 

 itself, nor in any of the causes on 

 which it depends. Every event is 

 in itself certain, not probable : if we 

 knew all, we should either know posi- 

 tively that it will happen, or positively 

 that it will not. But its probability 

 to us means the degree of expectation 

 of its occurrence, which we are war- 

 ranted in entertaining by our present 

 evidence. 



Bearing this in mind, I think it 



