An example of this I heard once is:<p>For a given car, there is no correlation between whether or not a car battery is dead or a fuel pump is broken.<p>However if you have a car that does not start, if you test the battery and it is working, you can now consider it more likely that the fuel pump is broken (because you have ruled out one cause of the car not starting, all other causes are now more likely).<p>This means that if you were to gather statistics about batteries and fuel pumps of all cars taken into the auto shop, you would find that there is a negative correlation between broken batteries and broken fuel pumps, despite this being clearly nonsensical for the general population.