Question 11.7.E.29: Work each problem. See Examples (1- 2 - 3 - 4 - 5 - 6). Male...
Work each problem. See Examples (1– 2 – 3 – 4 – 5 – 6).
Male Life Table The table is an abbreviated version of the 2010 period life table used by the Office of the Chief Actuary of the Social Security Administration. (The actual table includes every age, not just every tenth age.) Theoretically, this table follows a group of 100,000 males at birth and gives the number still alive at each age. Round answers to the questions that follow to the nearest thousandth.
Exact Age | Number of Lives | Exact Age | Number of Lives |
0 | 100,000 | 60 | 86,010 |
10 | 99,155 | 70 | 73,355 |
20 | 98,731 | 80 | 49,939 |
30 | 97,450 | 90 | 17,152 |
40 | 95,889 | 100 | 873 |
50 | 92,820 | 110 | 2 |
Source: Office of the Actuary, Social Security Administration.
(a) What is the probability that a 40-year-old man will live 30 more years?
(b) What is the probability that a 40-year-old man will not live 30 more years?
(c) Consider a group of five 40-year-old men. What is the probability that exactly three of them survive to age 70? (Hint: The longevities of the individual men can be considered as independent trials.)
(d) Consider two 40-year-old men. What is the probability that at least one of them survives to age 70? (Hint: The complement of at least one is none.)
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