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A medical example is described by Axelsson. Say a doctor performs a test that is 99% accurate, and the patient tests positive for the disease. However, the incidence of the disease is 1/10,000. The patient's actual risk of having the disease is 1%, because the population of healthy people is so much larger than the disease.
The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the belief that, if an event (whose occurrences are independent and identically distributed) has occurred less frequently than expected, it is more likely to happen again in the future (or vice versa).
The mathematics of gambling is a collection of probability applications encountered in games of chance and can get included in game theory.From a mathematical point of view, the games of chance are experiments generating various types of aleatory events, and it is possible to calculate by using the properties of probability on a finite space of possibilities.