Page 224 - Probability Demystified

CHAPTER 12 Actuarial Science 213

number living at 70
P(live to 70Þ¼
number living at 40
79,880
¼ ¼ 0:819
97,512
In other words, the probability of a 40-year-old female living to age 70 is
0.819, or about 82%.

EXAMPLE: How many males age 21 will die before age 65?

SOLUTION:
At age 21, there are 98,307 males out of 100,000 alive. At age 65, there are
78,410 males alive. Therefore, 98,307 78,410 ¼ 19,897 males have died
between the ages of 21 and 65. This is out of 98,307 who made it to age 21.

PRACTICE

1. Find the probability that a male will die at age 48.
2. On average, how many more years can a female who is age 56 expect
to live?
3. Find the death rate for a 63-year-old female.
4. What is the probability that a male age 43 will live to age 65?
5. What is the probability that a 25-year-old female will live to age 60?
6. Find the probability that a male will live to 21 years of age.
7. How many years longer can a female age 20 expect to live than a male
age 20?
8. About how many 2-year-old males will die before they reach 10 years
old?
9. What is the probability that a female age 16 will live to age 50?
10. Find the probability that a male will live to age 65.

ANSWERS

1. From the table, we see the probability that a male age 48 will die is
0.004859.
Alternate Solution: There are 92,790 males out of 100,000 males
age 48, and there are 92,339 males alive at age 49. So,
92,790 92,339 ¼ 451 males died at age 48.