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:Probability :Probability Axioms -- Probability Distributions The basic theorems of probability can be developed easily from the Probability Axioms and Set Theory. #The sum of the probabilities for all the elementary events is one. #For any arbitrary events, A1 and A2, the probability of both events, is given by the sum of the probabilities for all elementary events in both A1 and A2. If the intersection is empty, then the probability is exactly zero. #For any arbitrary events, A1 and A2, the probability of either or both, , is given by the sum of the probabilities of the two events minus the probability of both. The formulae below express the same ideas in algebraic terms. #SUM Pr[Ei] = 1 #Pr[A1*A2] = SUM of Pr[Ei] for all Ei in both A1 and A2. # Pr[A1+A2] = Pr[A1] + Pr[A2] - Pr[A1*A2] (in these equations, "+" means "or" and "*" means "and") The probability of some event happening knowing that another event happened before can be computed using Conditional Probability. |
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#REDIRECT Probability theory |
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