MegMeg's Nobel prize example is relevant to the board, but I can't resist pointing out that the example of this phenomenon that everybody needs to be aware of - because sadly, we have good research evidence* that most doctors completely fail to understand it, or at least to apply it correctly!! - is:
the probability that the test will be positive, given that you have the disease
is completely different from
the probability that you have the disease, given that the test is positive.
Doctors - i.e. even trained people who should know better - often treat these two as though they were the same, and hence overestimate the chance of disease by a lot (e.g., by a factor of 10).
* Gigerenzer, and Kahnemann and Tversky, have written about this extensively.
