exhibited in Tables of Statistics. 361 



Suppose, then, that with regard to the statistics of a certain 

 class of phsenomena we know nothing, except that during a series 

 of a years tlie number of such phtenomeua have been found to 

 be ab. 



Suppose these to be phtenomena presented by, or occurring to, 

 individuals in a population of n persons, which we shall suppose, 

 for the sake of simplicit}'^, to remain nearly constant during the 

 years in question. We will suppose also the phsenomena of a 

 kind which are not likely to occur to the same individual more 

 than once in the same year. Of this class would be most of the 

 important pluenomena of which tables of statistics furnish num- 

 bers. Now we suppose ourselves totally ignorant of the laws 

 which regulate such phfenomena, or rather we suppose it has 

 never occurred to us that they might be regulated by any laws. 

 Therefore we do not conceive the same ph?enomenon to be more 

 or less likely to be presented by the same individual in different 

 years than by different individuals. Consequently we may con- 

 ceive of the same individual in a different year, for the purposes 

 of this problem, as a different individual. 



Now using the word "probability" in its technical mathema- 

 tical sense, to say that we knoiv nothing except the above datum, 

 is the same as to say that the probability of a given person in a 

 given year presenting the phsenomenon is 



If we call this person Aj, we may now say that the probabiHty of 



Aj presenting the phsenomenon in the given year is -. 



Now suppose it known that A, presents the phsenomenon in 

 the given year ; to find the probability of a second given person 

 presenting it in the same year, we must remember that the num- 

 ber of remaining persons favourable to the supposition, any one 

 of whom the person given might be, is ab—\, and the whole 

 remaining number of persons is an—\. Therefore calling the 

 second given person Ao, the probability of A^ presenting the 

 phsenomenon in the given year is 



ab- \ 

 an — 1' 



and the probability of his not doing so is 



^ ab — 1 

 an — \' 



Therefore the probability of A^ presenting the phaenomenon in 



