Question

Probabilities of Death The US Social Security
Administration collects information on the
life expectancy and death rates of the population.
Table P.6 gives the number of US men out of
100,000 born alive who will survive to a given age,
based on 2011 mortality rates.6
For example, 50,344 of 100,000 US males live to
their 80th birthday.

(a) What is the probability that a man lives to
age 60?
(b) What is the probability that a man dies before
age 70?
(c) What is the probability that a man dies at age 90
(after his 90th and before his 91st birthday)?
(d) If a man lives until his 90th birthday, what is the
probability that he will die at the age of 90?
(e) If a man lives until his 80th birthday, what is the
probability that he will die at the age of 90?
(f) What is the probability that a man dies between
the ages of 60 and 89?
(g) If a man lives until his 60th birthday, what is the
probability that he lives to be at least 90 years
old?
Table P.6 Life Table for US males, 2011
Age 60 70 80 90 91
Number of lives 85,995 73,548 50,344 17,429 14,493

Answer 1

a) number of people that live atleast 60 = 85995
probability that a man lives to age 60 = 85995/100000 = 0.85995

b)
number of people who lives till 70 or above = 73,548
hence people who died before 70 is 100000-73,548 = 26452
probability that a man dies before age 70 = 26452/100000 = 0.26452

c)
people who died at 90 = 17,429 - 14493 = 2936
probability that a man dies at age 90 (after his 90th and before his 91st birthday) = 2963/100000 = 0.02963

d)
number of people who live by 90 = 17429
If a man lives until his 90th birthday, probability that he will die at the age of 90 = 2936/17429 = 0.16845487406

e)
number of people who live by 80 = 50,344
If a man lives until his 80th birthday, probability that he will die at the age of 90 = 2936/50344 = 0.05831876688

f)
number of people who dies between the ages of 60 and 89 = 85,995 - 17,429 = 68566
probability that a man dies between the ages of 60 and 89 = 68566/100000 = 0.68566

g)
people live till 60 years = 85995
If a man lives until his 60th birthday, probability that he lives to be at least 90 years old = 17,429 /85995 = 0.2026745741