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 p_{34} 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 “_{n}p_{x}”
that is, p with subscripts of n preceding and x following. It is read “n p x”. An example would be _{25}p_{40} 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 (_{n}p_{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 threeyear setback
for females, calculate the probability that a woman age 36 will live to reach
age 40.
Male Age (x)

l_{x}

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
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