PROBABILITIES OF LIVING:

The probability that a person age “x” will die in the next year is represented by the symbol q_x. The probability that a person age “x” will live to reach (x + 1) is represented by the symbol “p_x”.

That is. P with a subscript x. it is read “p sub x” or simply “p x”. An example would be p₃₄ which is read “p sub 34” or “p 34”. It means the probability that a person age 34 will live to reach age 35, that is, will be alive for at least one whole year.

In general terms, it may be said that if the number living at age (x + 1) is divided by the number living at age x, the result will be the probability that a person age x will live to reach age (x + 1). In equation form, this is written as:

The result shows that, according to this particular table, the probability that a person age 20 will live for at least one year is 0.8885.

The result shows that, according to this particular table, the probability that a person age 50 will be live at least one year is 0.9909.

PROBABILITIES OF LIVING FOR n YEARS:

The concepts presented above can be extended to include the probabilities of a person living for any numbers of years, or dying within any number of years. The probability that a person age x will live at least n more years, or that the person will reach age (x+ n), is represented by the symbol “_np_x” that is, p with subscripts of n preceding and x following. It is read “n p x”. An example would be ₂₅p₄₀ which is read “15 p 20”. It represents the probability that a person age 40 will live at least 25 more years, that is, that the person will reach age 65.

The probability that a person age x will live at least n more years (_np_x) is found by dividing the number living at age (x + n) by the number living at age x. In equation form this is written as:

To Illustrate: Using the following portion of a mortality table, calculate the probability that a person age 24 will live at least six more years.

The probability that a person age 24 will live at least six more years is 0.9184.

To Illustrate: using the following portion of a male mortality table and a three-year setback for females, calculate the probability that a woman age 36 will live to reach age 40.

Male Age (x)	lx
33	9209
34	9173
35	9135
36	9094
37	9049
38	9001
39	8948
40	8891

Solution:

Three years must be subtracted from the ages before using the table. This means using the table as if calculating the probability of a male age 33 reaching age 37. The number of years involved, n is 4

Basic equation