We have already observed, that the doctrine of chances is particularly appli cable to the business of life annuities and assurance. This depends on the chance of life in all its stages, which is found by the bills of mortality in different places. These bills exhibit how many persons up on an average out of a certain number born are left at the end of each year, to the extremity of life. From such tables the probability of the continuance of a life of any proposed age is known.
Example. To find the probability that an individual of a given age will live one year. Let A be the number in the tables of the given age, B the number left at the endof the year; is the probability that the individual will live one year; and B A— — the probability that he will die in A that time. In Dr. Halley's tables, out of 586 at the age of 22, 579 arrive at the age of 23 ; hence the probability that an indi 579 vidual aged 22 will live one year is or 83 7 1 ; and-- or —nearly is the pro 586 84 bability that he will die in that time. See MORTALITY, bills Of &C.
Those who would enter more at large into this subject may be referred to the works already mentioned, or to the arti cle CHANCES in the new Cyclopedia of Dr.
Rees, a work that will be found in every library of general literature, and in which this subject is treated with great ability. Though we shall under the article GAM mu refer again to the doctrine of chances, it may not be amiss to mention a deduc tion or two, drawn by the writer of the article just referred to, as the necessary consequences of mathematical reasoning. The first is : suppose a lottery consist ing of 25,000 tickets, of which 20 are to be prizes of 10001. and upwards ; a per son, to have an equal chance of one of those prizes, must purchase about 870 tickets, which at 20/. each is equal to 17,400/. • Again : suppose there are three prizes of 20,000/. and three of 10,0001. and a person out of 25,000 ticketshas purchased 3000 of them to his own share, in hopes of gaining one of each of these capital prizes ; still the chances against such an expectation will be nearly twelve to one. See GAMING.