----- . . . that something can be true of every subset but not of the whole set. ----- That's not quite how Simpson's paradox is usually stated. The Wikipedia article at https://en.wikipedia.org/wiki/Simpson's_paradox has some nice examples. —Dan -----Original Message-----
From: "Keith F. Lynch" <kfl@KeithLynch.net>
My favorite probability paradox is Simpson's paradox, i.e. that something can be true of every subset but not of the whole set. A surprising real-world example is that until recently US life expectancy was going up, but that there were two groups for which it was going down: Smokers and non-smokers.
The explanation is that, roughly speaking, life expectancy was only increasing because of people quitting smoking, and that all else was a net loss, presumably because improvements in medical care were more than offset by the increasing unaffordability of that care.
Of course it's not really a paradox, just an example of how mathematical intuition is often wrong.
thanks, these are great - but I’m looking for things that are even more basic, like Veit’s calculation of poker hand probabilities. (I can also start with dice outcomes.) - Cris
On Mar 25, 2017, at 11:20 AM, Dan Asimov <dasimov@earthlink.net> wrote:
----- . . . that something can be true of every subset but not of the whole set. -----
That's not quite how Simpson's paradox is usually stated.
The Wikipedia article at https://en.wikipedia.org/wiki/Simpson's_paradox has some nice examples.
—Dan
-----Original Message-----
From: "Keith F. Lynch" <kfl@KeithLynch.net>
My favorite probability paradox is Simpson's paradox, i.e. that something can be true of every subset but not of the whole set. A surprising real-world example is that until recently US life expectancy was going up, but that there were two groups for which it was going down: Smokers and non-smokers.
The explanation is that, roughly speaking, life expectancy was only increasing because of people quitting smoking, and that all else was a net loss, presumably because improvements in medical care were more than offset by the increasing unaffordability of that care.
Of course it's not really a paradox, just an example of how mathematical intuition is often wrong.
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i like the fact that when 6 six-sided dice are thrown, the probability that exactly 4 different numbers appear amongst them is greater than 1/2. On Sat, Mar 25, 2017 at 11:02 AM Cris Moore <moore@santafe.edu> wrote:
thanks, these are great - but I’m looking for things that are even more basic, like Veit’s calculation of poker hand probabilities. (I can also start with dice outcomes.)
- Cris
On Mar 25, 2017, at 11:20 AM, Dan Asimov <dasimov@earthlink.net> wrote:
----- . . . that something can be true of every subset but not of the whole set. -----
That's not quite how Simpson's paradox is usually stated.
The Wikipedia article at https://en.wikipedia.org/wiki/Simpson's_paradox has some nice examples.
—Dan
-----Original Message-----
From: "Keith F. Lynch" <kfl@KeithLynch.net>
My favorite probability paradox is Simpson's paradox, i.e. that something can be true of every subset but not of the whole set. A surprising real-world example is that until recently US life expectancy was going up, but that there were two groups for which it was going down: Smokers and non-smokers.
The explanation is that, roughly speaking, life expectancy was only increasing because of people quitting smoking, and that all else was a net loss, presumably because improvements in medical care were more than offset by the increasing unaffordability of that care.
Of course it's not really a paradox, just an example of how mathematical intuition is often wrong.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (3)
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Cris Moore -
Dan Asimov -
Thane Plambeck