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In the discrete world of probability theory, assigning probability involves systematically allocating numerical values to the outcomes of an experiment in such a way that these values reflect the likelihood of occurrence of each outcome and satisfy the fundamental axioms of probability. The procedure begins with a clear identification of the random experiment and the construction of the sample space, which is the set of all possible outcomes. In a discrete setting, the sample space consists of either a finite or a countably infinite number of outcomes, such as the outcomes of tossing a coin, rolling a die, or counting the number of arrivals in a queue. Once the sample space is defined, the next step is to determine the events of interest. An event is any subset of the sample space, including single-element subsets (elementary events) and combinations of outcomes. Assigning probability requires defining a probability function that maps each event, particularly each elementary outcome, to a real number between 0 and 1. This mapping must adhere to the axioms established by Kolmogorov, which form the foundation of modern probability theory. These axioms state that the probability of any event is non-negative, the probability of the entire sample space is equal to one, and the probability of a countable union of mutually exclusive events is equal to the sum of their individual probabilities. A practical and intuitive method of assigning probability in discrete cases is the classical or equally likely approach. This method is applicable when all outcomes in the sample space are considered equally likely to occur. In such situations, the probability of an event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. For example, when rolling a fair die, each of the six outcomes has an equal probability _____ ___ _________ ______ ______ ___ ______ ________.
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