MATHEMATICS. 25 



half of the remainder is the average time that a man 

 may expect to live. Thus years 



Boundary of human life - - 86 

 Suppose an individual's age to be 40 



Average expectation of life - Years 23 



The period of life at which man (under all circum- 

 stances) has the probability of the greatest number 

 of years to come, is the age of 33. 



If the probability that one man, A, shall live a 

 year be T ^ and the probability of the life of another 

 man, B, for one year be T ^, the probability that both 

 shall live another year is as 100 to 48 ; viz. 



. 



The probability of the death of A within the year 

 being 1 %, and of the death of B T ^, the probability 

 that both shall die within the year is -^ x -fsi^-Q' 



The probability that one of the events shall hap- 

 pen and the other fail, is, as the probability of the 

 happening of the one, multiplied by the probability of 

 the failure of the other. So in the above case, the 

 probability that A shall live and B die is -^ x j%= 

 ^ ; and the probability that B shall live and A die 

 is ft X ft=-flfr. 



Chance. 



Chance very little disturbs events, which in their 

 natural constitution were designed to happen or fail 

 according to some determined law. It may produce 

 the appearance of inequality in the turning up of the 

 head or reverse of a coin, still the appearance, one 

 way or another, will perpetually tend to the propor- 

 tion of equality. Thus in all cases it will be found, 

 that although chance produces irregularities, still the 

 odds will be infinitely great, that in process of time 

 these irregularities will bear no proportion to the 



