from the Mathematical Theory of Probabilities. 515 

 Prob. of event x in any part of the Universe of type x n ~ r x r 



n — r 



n 

 Prob. of the Universe having that type 



2 n \r n — r 



E. g. Prob. of such a Universe that x happens n—1 times 

 and does not happen once, i. e. prob. that this conjunction occurs, 



n 



= 2^ 



and so on. In general, 



Prob. that x happens n—r times, and does not happen r times 

 = Prob. of Universe having the type x n ~ r x r , 



2 n \r \n — r 

 Also we have 



Prob. that if x happens n—1 times, it does not happen once 



__ Number of constitutions x n ~ l x 



Number of const. x n + Number of const. x n ~ l x 



and Prob. that it does happen this once also 

 1 



.\ in the unknown case 



prob. of occurrence : prob. of non-occurrence = 1 : n. 

 (This result should be noted.) 



But the case is different if x be supposed to happen n — 1 

 times running and not the wth, i. e. where x can only appear 

 in the last place, as in x x x x . . . x. This constitution occurs 

 once only among the n constitutions of type x n ~ l x. 



.\ Prob. that if x has happened n — 1 times it does not the 

 nth. time 

 _ Number of constitutions (x x x . . . ) n ^ l x 



~~ Number of const, (x x . . . ) n _! x + Number of const. x n 



= = — =- = ~ = absolute ignorance. 

 1 + 1 2 to 



