|
|
#41
07-08-2004, 02:02 PM
|
|||
|
|||
Answer
Its 110-112. Anybody who said less than the mid 100s wasn't thinking clearly. Because if there is a greater than one half chance of dying in one year, than the probability of surviving ten years would be much less than one in 1024. Since there is only a few tens of thousands of Americans in their early 100s, and several 110 or above, that would disprove that guess.
|
|
#44
07-08-2004, 10:49 PM
|
|||
|
|||
|
Re: Answer
The oldest person in the U.S. just died a few weeks ago at 114. As the problem is stated, you could figure that of the two oldest people at any given time, one (one half or 50%) will probably die within a year. 50% dying gets less likely as numbers get larger as you move the age down. I don't know how old the two oldest people in the U.S. are right now but the 110 - 112 is probably close. I saw the answer before I could put a guess in but would have estimated 112 based on above thinking.
|
|
#46
07-08-2004, 11:26 PM
|
|||
|
|||
|
Re: Answer
Quote:
-------------------------------------------------------------------------------- How would we know how many people there are 110 years of age or older, or how many there are 100? -------------------------------------------------------------------------------- Apparently, we can figure this out by thinking clearly. Pure thinking can in fact get you close for 100 year olds.
|
|
#47
07-09-2004, 01:22 AM
|
|||
|
|||
|
Re: Answer
think about it.....
if you know someone who is 75 years old do you really think there is a 50-50 shot he will die within a year?? if so then there is preseumably a slightly better than 50-50 shot that he will die the next year....and the year after that...etc etc. even if it stays at 50/50 each year then posting a guess of 75 means that any 75 year old person only has around a 1:1000 (2^10 = 1024) chance of living until 85. and about a 1:1,000,000 chance of living until 95. i have grandparents who are 85 and 88.....so if the 50-50 cutoff was really 75 then my grandparents had REALLY beat the odds. obviously they have done pretty well overall....but i know i'm not the only one on here with GP's in their mid or late 80's. i also had 3 great-grandparents who lived into their 90's...just rounding off to 1:1-million for each, the odds of having 3 great-GP's all live into their 90's would be ridiculously high. so you don't need to know how old the oldest living person in the world is or how many 100 year olds there are in the US....basic common sense plus the math should get you reasonably close. however, i admit it is a bit easier to make all these grand statements AFTER joining the thread a bit late. i probably would have been super-screwy without the ability to read the other replies and david's answer before i posted. anyway..... interesting little brain-tease david. albeit a freaking morbid one. i also found it interesting the number of people who responded 0 or 1.
|
|
#48
07-09-2004, 01:37 AM
|
|||
|
|||
|
It\'s right around 100!
Very neat puzzle! Thank you for posting it. [ QUOTE ] Because if there is a greater than one half chance of dying in one year, than the probability of surviving ten years would be much less than one in 1024. Since there is only a few tens of thousands of Americans in their early 100s, and several 110 or above, that would disprove that guess. [/ QUOTE ] Assuming your facts & a half-life distribution, we actually get right around 100 (maybe 98-102, as many posters sensibly guessed) as the answer. Here's why: "A few ten thousands in their early hundreds" gives about 10,000 at exactly age 100. At 100+, it might be that the constant risk of death stops increasing much because the death rate is asymptotically maxing out (the organism is already so dangerously superannuated...). 2-to-the-10th is 1024, so 10,000 exactly-100-year-olds degrades to 10,000/1,024 = about 10 exactly-110-year-olds... which in turn degrades to about 5 exactly-111-year-olds... and about 2 exactly-112-year-olds... which perfectly fits your facts of only 'several' Americans at 110 or above! So, 'pure thought' should actually give an answer of around 100 to fit those facts & assumptions you so far have spelled out. {In biological reality, though, the human species has much more diversity -- 'heavier tails' (of mathematical distributions) in most measurable respects -- than a bell curve or half-life-type-degradation has. For example, there are a lot more humans at IQ>160 than a single true normal Gaussian bell curve centered at 100 with a standard deviation of 15 would produce. So, 'pure thought'-type answers here need to include wide ranges for uncertainty! Humanity has enough strange subpopulations with their own skewed distribution curves -- including some Okinawans & Ukrainians with respect to aging -- that I wouldn't even be surprised if your question in reality has a couple correct answers (two or more places where Americans lumped as one population cross the 50%/year-chance-of-death line!). }
|
|
#49
07-09-2004, 02:31 AM
|
|||
|
|||
|
...99 is a better estimate if death rate has gone ~asymptotic by then
I wrote,
[ QUOTE ] "A few ten thousands in their early hundreds" gives about 10,000 at exactly age 100. [/ QUOTE ] ...but it's more like about 20,000 at exactly 100 for a total of almost 40,000 in their early 100s. So, shift all the years down by 1.
|
|
#50
07-09-2004, 02:55 AM
|
|||
|
|||
|
Life Expectancy Chart
From this chart,
Age # of yrs the IRS expects you to live: 103 2.1 104 1.9 105 1.8 106 1.6 107 1.4 108 1.3 109 1.1 110 1.0 it looks like the real answer is somewhere around 110. (assuming 'expected years to live' is the same concept as our beloved 'EV') It's not easy to tell exactly though. Do you see why? Also, importantly, this chart (if even approximately accurate) shows that my 'asymptotic risk' assumption doesn't describe real Americans in this age range. That's what I got for 'pure thought' here [img]/images/graemlins/wink.gif[/img]
|
 |
|
|
Linear Mode
