Re: [math-fun] probability

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.