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A number between and inclusive of zero and one indicating the likelihood of an event. Two kinds of probabilities are distinguished. (1) The logical interpretation of probability indicates how easy it would be to select one designated or preferred alternative out of a given set of possible alternatives (see degree of freedom). (2) The frequency interpretation of probability indicates how often a particular event is observed relative to all observed events. Whereas (1) is concerned with possibilities and makes no references to actual observations, (2) is concerned only with what was observed, not with what could be but wasn't. Despite the fundamental differences between the two, both conform to the same laws of probability theory. Let M be a set of elements (possibilities or observations). With 0 as the empty set. The probabilities of subsets A of M range between:

0 < P(A) < 1

For any set A and its complement A in M:

P(A and not A) = P(0) = 0
P(A or not A) = P(M) = 1

and for mutually exclusive sets A_i:

P(A_1 or A_2 or...) = P(A_1) + P(A_2) +....

the space of possibilities on the one side and the sample size of observations on the other assure that probabilities add up to 1. (Krippendorff)

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