Just recently, my Uncle Joe celebrated his 96th birthday. I called him and wished him the best, and he was glad to hear from me. It got me thinking again about how my grandfather, my father, and all of my Uncles on my father’s side lived very long lives, much longer than the average. While this side of my gene pool has longevity, my mother’s side is almost the opposite, so I’ll do well to make 80.
I will only use first names here for personal reasons and to protect my uncles' personal information. The table below lists my grandfather and uncles by their first names as well as their birth months and death months:
- Grandfather Filippo, Oct 1885 to Dec 1979, 34,379 days, 94y 1m 16d
- Uncle Tony, Jan 1910 to Mar 1996, 31,478 days, 86y 2m 7d
- Uncle Neno, Mar 1921 to Jan 2009, 32,105 days, 87y 10m 22 d
- Dad, Apr 1926 to Feb 2023, 35,356 days, 96y 9m 17d
- Uncle Joe, Apr 1928 to Not deceased (as of Jun 1, 2024), 35,097, 96y 1m 3d
- Uncle Bill, Nov 1929 to Not deceased (as of Jun 1, 2024), 34,548 days, 94y 7m 2d
I thought this was a great question to pose to an AI (Artificial Intelligence) and have it calculate the probability of all these men living so long. While I don’t know if it is 100% accurate, my schooling in probability and statistics confirms that what it says is reasonable.
Here is the prompt I gave the OpenAI GPT named “Automated Writer.”
Here is the output:
The Longevity of My Family: A Statistical Perspective
Introduction
When pondering the remarkable longevity of my grandfather, father, and uncles, it’s fascinating to consider the statistical probability of their long lives. This post delves into their life spans and examines how they compare to historical life expectancy data.
Family Longevity Overview
- Grandfather: Born in 1885, lived until 94.
- Father: Born in 1926, lived until 96.
- Uncle Tony: Born in 1910, lived until 86.
- Uncle Neno: Born in 1921, lived until 87.
- Uncle Joe: Born in 1928, 96 as of June 1, 2024.
- Uncle Bill: Born in 1929, 95 as of June 1, 2024.
Life Expectancy Context
Historical Life Expectancy
- 1885: Average life expectancy in the U.S. was approximately 40-45 years.
- 1910: Average life expectancy was about 50-55 years.
- 1920s: Average life expectancy was around 55-60 years.
Family Longevity Statistics
- Grandfather: 94 years (exceeded life expectancy by ~50 years).
- Father: 96 years (exceeded life expectancy by ~40 years).
- Uncle Tony: 86 years (exceeded life expectancy by ~30 years).
- Uncle Neno: 87 years (exceeded life expectancy by ~30 years).
- Uncle Joe: 96 years (exceeded life expectancy by ~40 years).
- Uncle Bill: 95 years (exceeded life expectancy by ~40 years).
Probability Analysis
- Understanding Mortality Rates: Life expectancy averages don’t fully capture the individual probability of living to advanced ages. Mortality rates decline with each passing year one survives, meaning those who reach older ages often continue to live longer.
- Family Genetics and Lifestyle: The likelihood of longevity can be influenced by genetics and lifestyle. Families with histories of long lives often have genetic advantages.
Survival Curves and Cohort Analysis
Early 20th Century: Survival curves typically showed steep drops due to high infant mortality, with a flattening out for those reaching adulthood. For example, those who reached 60 had better odds of living into their 70s and beyond.
Relative Probability:
- For someone born in the 1880s, reaching 94 was highly uncommon but possible. Historical data suggests very low single-digit percentages.
- By the mid-20th century, reaching 80s and 90s became more common but still relatively rare.
Here is where the initial response ended. While I was provided some interesting information, it did not provide me with the probability that I asked for, so I submitted the following prompt:
Here is more output based on the second prompt.
Historical Context
We need to use actuarial life tables from different periods to estimate these probabilities. These tables show the likelihood of surviving at a particular age.
Life Tables and Probabilities:
- Grandfather (Born 1885): Life expectancy at birth is around 40 years.
- Father (Born 1926): Life expectancy at birth is around 60 years.
- Uncle Tony (Born 1910): Life expectancy at birth is around 50 years.
- Uncle Neno (Born 1921): Life expectancy at birth is around 55 years.
- Uncle Joe (Born 1928): Life expectancy at birth is around 60 years.
- Uncle Bill (Born 1929): Life expectancy at birth is around 60 years.
Survival Rates:
- Survival rates improve significantly if an individual reaches adulthood.
- For example, the probability of a man born in 1885 living to 60 might be around 25%, and the probability of living from 60 to 94 would be considerably lower.
Calculations:
Using survival rates from historical actuarial tables, we can approximate the probabilities. Here’s a simplified example:
Grandfather:
- Probability of reaching 60 years if born in 1885: ≈ 25
- Probability of living from 60 to 94: ≈ 10%
- Combined probability: 25% * 10% = 2.5%
Father:
- Probability of reaching 60 years if born in 1926: ≈ 60%
- Probability of living from 60 to 96: ≈ 5%
- Combined probability: 60% * 5% = 3%
Uncle Tony:
- Probability of reaching 60 years if born in 1910: ≈ 45%
- Probability of living from 60 to 86: ≈ 20%
- Combined probability: 45% * 20% = 9%
Uncle Neno:
- Probability of reaching 60 years if born in 1921: ≈ 50%
- Probability of living from 60 to 87: ≈ 15%
- Combined probability: 50% * 15% = 7.5%
Uncle Joe:
- Probability of reaching 60 years if born in 1928: ≈ 60%
- Probability of living from 60 to 96: ≈ 5%
- Combined probability: 60% * 5% = 3%
Uncle Bill:
- Probability of reaching 60 years if born in 1929: ≈ 60%
- Probability of living from 60 to 95: ≈ 5%
- Combined probability: 60% * 5% = 3%
Combined Probability
To find the combined probability of all these events occurring, we multiply the individual probabilities:
P{combined) = P(Grandfather) x P(Uncle Tony) x P(Uncle Neno) x P(my father) x P(Uncle Joe) x P(Uncle Bill)
P(combined) = 0.025 x 0.09 x 0.075 x 0.03 × 0.03 x 0.03
P(combined) = 0.00000000455625
The combined probability is approximately 0.000000456% (or, to put it another way, a 1 in 219,478,738 chance of this occurring), which is extraordinarily low. This statistical rarity underscores just how remarkable their lives have been.
