204 ESSAY ON PROBABILITIES. 



tion of the problem. Thus, suppose it required to 

 represent the value of an annuity which is to continue 

 as long as any two of the three, A, B, and C, are alive. 

 This must be done thus : 



| AB: AC: BC 



This might be abbreviated into | (ABC) , or any such 

 symbol; which, however, I should recommend to no 

 one who is not very familiar with the developed form. 



A method of making the notation of chances analogous 

 to that of annuities was devised by Mr. Milne, which is 

 much too ingenious and efficient to allow of its being 

 dispensed with in any future system. To adapt the 

 principle of this connexion to the system which I have 

 proposed, let n^a express the chance that A shall be 

 alive in n years, in which the smah 1 letters answering to 

 the capitals which denote lives refer to the chances 

 of those lives, and certain letters m, n, t (or more 

 if necessary), are reserved to signify terms of years. 

 Then all which precedes the sign t (or any other which 

 may be preferred), refers to lives or terms expired, and 

 those which follow the sign, to lives or terms which 

 are to be then in existence. Where no given term of 

 years is included, the chance must be understood to 

 refer to the whole continuance of all the status mentioned. 

 Thus, 



t& is the chance that A shall die before B. 



a wt6 is the chance that one of the two, A or n years, 

 shall fail before B. 



a : n^b is the chance that both A and n years shall 

 fail before B ; that is, that B shall outlive A, and also 

 live more than n years. 



a^n the chance that A shall not survive n years. 



a : n^b the chance that A shall die in n years, and 



that B shall outlive that term. 



e chance that the joint existence of A and 

 B (or both A and B) shall outlast n years. 



n: a 4- (71 -fl) the chance that A shall die in the 



1 2 



(n -}- 1 )th year from this time. 



