V. On the Calculation of Annuities, and on some 

 Questions in the Theory of Chances. 



By J. W. LUBBOCK, Esq. B.A. 



[Read May 26, 1828.] 



Ihe object of the following: investigation is to shew how 

 the probabilities of an individual living any given number of 

 years are to be deduced from any table of mortality. All writers 

 (with the exception of Laplace) have considered the probability 

 of an individual dying at any age to be the number of deaths 

 at that age recorded in the table, divided by the sum of the 

 deaths recorded at all ages. This would be the case if the 

 observations on which the table is founded were infinite, but 

 the supposition differs the more widely from the truth the less 

 extended are the observations, and cannot, I think, be admitted, 

 where the recorded deaths do not altogether exceed a few thousand, 

 as is the case in the tables used in England. The number of 

 deaths on which the Northampton tables are founded is 4689, 

 (Price, Vol. I. p. 357.). The tables of Halley are founded ujion 

 the deaths which took place at Breslaw in Silesia during five 

 years, and which amounted to 5869. 



If a bag contain an infinite number of balls of different colours 

 in unknown proportions, a few trials or drawings will not indicate 

 the proportion in which they exi.st in the bag, or the simple 

 probability of drawing a ball of any given colour, and not only 



