Application of the Theory of Probabilities to the Mortality Table

The statement was made earlier in this chapter that risk in life insurance is measured by the application of the laws of probability to the mortality table. Now that these laws are understood and the mortality table has been explained, a few simple illustrations may be used to show this application. Suppose it is desired to insure a man aged 35 against death within one year, within two years, or within five years. It is necessary to know the probability of death within one, two, or five years from age 35. This probability, according to the laws heretofore explained, will be determined according to the mortality table and will be a fraction of which the denominator equals the number living at age 35 and the numerator will be the number who have died during the one, two, or five years, respectively, following that age. According to the table, 81,822 persons are living at age 35, and 732 die before the end of the year. Hence the probability of death in one year is 732/81822. During the two years following the stated age there are 732 + 737 deaths, or a total of 1,469. The probability of dying within two years is therefore 1469/85822. Likewise the total number of deaths within five years is 732 + 737 + 743 + 749 + 756 or 3,716, and the probability of dying within five years is thus 3716/81822.

Probabilities of survival can also be expressed by the table. The chance of living one year following age 35 will be a fraction of which the denominator0 is 81,822 and the numerator will be the number who have lived one year following the specified age. This is the number who are living beginning age 36, or 81,090, and the probability of survival for one year is therefore 81090/81822. These illustrations furnish an opportunity for a proof of the law of certainty. The chance of living one year following age 35 is 81090/81822 and the chance of dying within the same period is 732/81822. The sum of these two fractions equals 81822/81822 or 1, which is certainty, and certainty represents the sum of all separate probabilities in this case two, the probability of death and the probability of survival. In like manner many more instructive examples of the application of these laws to the mortality table could be made, but they need not be carried further at this point, for the subject will be fully covered in the chapters on "Net Premiums".