An Insurance Office, which, in consideration of fixed premiums undertakes the payment of a sum on the death of the assured, strictly speaking lays a wager with each of the assured, in which the stakes are proportional to the probabilities of the happening of the two contrary events—his living and his dying. Every assurance of a sum payable at death admits of being divided into partial assurances for a fixed period, as a year. Let the sum assured be S and the probability of death within a year p, then pS will be the stake of the assured, or the premium; and (1−p)S the stake of the office, i.e. the amount which the office would lose in case of the death of the assured within the year. The two stakes together therefore amount to the sum assured.