Page 223 - Probability Demystified

212 CHAPTER 12 Actuarial Science

EXAMPLE: Find the death rate for 30-year-old males.

SOLUTION:
From the table for a 30-year-old man, there are 97,129 out of 100,000
living, and for age 31, there are 96,999 males living; hence, 97,129 96,999,
or 130 males died during their 30th year of life. Now the death rate is
130 males out of a total of 97,129 or
number who died during the year
P(dying at 30) ¼
number living at the beginning of year 30
130
¼ 0:00133
97,129
Notice that the table gives a value of 0.001396 under the column ‘‘Death
probability.’’ The reason for this discrepancy is probably due to the fact that
samples larger than 100,000 males were used in the calculation, or perhaps
it is due to rounding.

EXAMPLE: What is the probability that a male age 25 will die before age 60?

SOLUTION:
The number of males living at age 25 is 97,760 out of 100,000, and the num-
ber of males living at age 60 is 84,682. So to find the number of males who
died, subtract the two numbers: 97,760 84,682 ¼ 13,078. That is, 13,078
males died between age 25 and age 60. Next, find the probability.
number who died
P ¼
number living at the beginning of year 25
13,078
¼ 0:134
97,760
In other words, there is about a 13% chance that a male age 25 will die
before age 60.

EXAMPLE: What is the probability that a female who is 40 will live to the
age of 60?

SOLUTION:
At age 40 there are 97,512 females out of 100,000 alive. At age 70, there are
79,880 females alive. Hence,