174 ESSAY ON PROBABILITIES. 



Persons who are desirous of using tables of life on a 

 larger scale, are referred to the standard works of Messrs. 

 Morgan, Baily, and Milne, on life insurance. In the pre- 

 sent work I assume that it will be sufficient to be within 

 two years and a half of any age which may be named, and 

 I have given the several tables for intervals of five years. 

 The extremes which are used by actuaries generally 

 being contained in the Carlisle and Northampton tables, 

 and having given the former, I now add the latter. 

 The first column contains the age, the second the table 

 of decrements, the third the number out of 10,000 who 

 die in one year after completing the age in the first 

 column. 



Supposing the tables perfectly accurate, the following 

 simple questions will show the nature of the first steps 

 which occur in their application. The Carlisle tables 

 are used throughout. 



Question 1. What is the chance that an individual 

 aged 35 will live to the age of 50 ? Of 5362 persons 

 aged 35, 4397 live to be 50; hence the chance in 

 question is -|--||-J or '82. Answer, 41 to 9 for the 

 event. 



Question 2. What is the chance that A aged 45 

 and B aged 50, shall both be alive in ten years ? The 

 chance for A, by the last question, is |4f|-f> or '862 

 and that for B ||-^| or '829 ; the product of these 

 (p. 43.), or '715, is the chance required. Again, the 

 chances of A and B dying during the ten years are 

 1 -862 and 1 '829, or -138 and -171 ; whence, 



