Kolomogrov laws

Terms from Statistics for HCI: Making Sense of Quantitative Data

A collection of three axioms developed by Andrey Kolmogorov in 1933, which summarise the laws of probability. The three axioms state that (i) the probability of any set of events is greater than or equal to zero (you can't have a negative chance of doing something); (ii) the probability of the set of all events is one (the probability that something will happen is one); and (iii) the probability of the union of disjoint sets of events is the sum of the probability of each set (probabilities add up when there is no overlap). For example, if we throw a (possibly loaded) die, the sets of events are subsets of {1,2,3,4,5,6}. Axiom (i) says, inter alia, that Prob({1,2}) > 0 (meaning the probability of either a 1 or 2); axiom (ii) says that Prob({1,2,3,4,5,6})=1; and axiom (iii) that, inter alia, Prob( Union({1,2},{3,6}) ) =Prob( {1,2,3,6}) = Prob({1,2}) + Prob({3,6}).

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