I don't think your two racial profiling examples are so much a problem of conflating statistics and probability, as they are a problem of confusion of the inver

I don't think your two racial profiling examples are so much a problem of conflating statistics and probability, as they are a problem of confusion of the inverse (http://en.wikipedia.org/wiki/Confusion_of_the_inverse http://en.wikipedia.org/wiki/Confusion_of_the_inverse). It is the case that if you randomly select an illegal immigrant in the US, then the expectation (p ≈ 75%) is that they will be Hispanic. That's not a misapplication of statistics; it's just what the numbers say. However, that does not mean that if you randomly select a Hispanic person, the expectation is that they are an illegal immigrant. The probability is in fact closer to 15%. The imbalance of those numbers for people who "look like terrorists" at airports is even more preposterous, of course. But statistical invalidity is not the only reason that racial profiling is bad. Even if 99% of Hispanic people really were illegal immigrants, it would be unacceptable for police to target them based on race. Not because it would be an invalid conflation of statistics and probability - it wouldn't. The problem is that in order to protect individual rights, the police and the courts must not act strictly according to expectation. We shouldn't imprison someone, for example, just because we reckon there's a 75% chance they were the killer. And if 99% of Hispanic people were illegal immigrants, and so police hassled every Hispanic person, then we would know just as sure as we'd know that they'd have a 99% success rate, that they'd be violating the civil rights of the other 1%.