One way to differentiate between probability and statistics posits that there is an inverse relationship between the problems considered by the two fields (the explanation is often attributed to mathematician Persi Diaconis). With probability, one studies an essential activity that includes some degree of randomness or uncertainty, and one uses probability to figure out what is likely to happen in certain circumstances. With statistics, something that has already happened is observed; the statistician hope to figure out the underlying process that provided the result. Thus probability deals with predicting the likelihood of future events, while statistics involves the analysis of past events.
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