ON LIFE CONTINGENCIES. HJ5 



The chance is 



That both shall live '862 x -829 



That A shall live and B die -862 x -171 

 That A shall die and B live -138 x -829 

 That both shall die '138 x -171 



Question 3. What is the chance that A aged 25, 

 shall die between the ages of 60 and 65 ? Of 5879 

 persons aged 25, 36433018 or 625,, die between the 

 ages of 60 and 65 ; hence / is the chance re- 

 quired. 



Questions of this kind are readily solved, the only 

 impediment being the arithmetical operation. It fre- 

 quently happens, however, that the probability of one 

 individual surviving another is required, which though 

 an even chance when the individuals are of the same 

 age, is a matter of considerable calculation when one is 

 older than the other. Suppose, for example, that the 

 chance of A (aged 25) surviving B (aged 30) is required. 

 The survivorship, as it is called, meaning the period 

 during which A lives after the death of B, may begin 

 in any one year of A's age. For each year the pro- 

 bability of the survivorship beginning in that year must 

 be calculated. To make this calculation for one in- 

 dividual year, say that in which A is between 49 and 

 50, two cases must be considered : either B may die 

 between 54 and 55, and A may attain 50 complete 

 years (of which the chance may be found as in the 

 preceding questions), or both may die in the same year 

 (that is A between 49 and 50, and B between 54 and 

 55), but B may die first. If the chance of both dying 

 in that year be, say,'012,it is sufficiently correct to con- 

 sider the half of this chance, or '006, as being that which 

 expresses the chance of A's survivorship both beginning 

 and ending in that year : # supposition which is quite 

 correct only when the deaths of the year are equally 

 distributed through it. The result of this calculation 

 is arranged in tables, of which I here give a brief 

 abstract. 



