--------------------------------------------- S13h. How do probabilities apply in practice? --------------------------------------------- If one has a sound probabilistic model of a multitude of independent events e_i with same assigned probability p one would be surprised if the frequency of events is not close to p within a small multiple of sqrt(p(1-p)/N). Rather than just accepting a rare occurence (e.g., a brick going upwards due to fluctuations) as something within one's probabilistic model, one would probably rather try to explain it away by assuming a hidden, unobserved cause (someone throwing it). The way probabilities are used in practice is always as informative guides of what to expect, but not as statements with a 100% exact meaning. I wrote a paper on surprise: A. Neumaier, Fuzzy modeling in terms of surprise, Fuzzy Sets and Systems 135 (2003), 21-38. http://www.mat.univie.ac.at/~neum/papers.html#fuzzy that may help understand the fuzziness inherent in our concepts of reality.