General Computational Probability Rules-ECO6416

General Computational Probability Rules-ECO6416 - General...

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General Computational Probability Rules 1. Addition: When two or more events will happen at the same time, and the events are not mutually exclusive, then: P (X or Y) = P (X) + P (Y) - P (X and Y) Notice that, the equation P (X or Y) = P (X) + P (Y) - P (X and Y), contains especial events: An event (X and Y) which is the intersection of set/events X and Y, and another event (X or Y) which is the union (i.e., either/or) of sets X and Y. Although this is very simple, it says relatively little about how event X influences event Y and vice versa. If P (X and Y) is 0, indicating that events X and Y do not intersect (i.e., they are mutually exclusive), then we have P (X or Y) = P (X) + P (Y). On the other hand if P (X and Y) is not 0, then there are interactions between the two events X and Y. Usually it could be a physical interaction between them. This makes the relationship P (X or Y) = P (X) + P (Y) - P (X and Y) nonlinear because the P(X and Y) term is subtracted from which influences the result. The above rule is known also as the Inclusion-Exclusion Formula . It can be extended to more than two events. For example, for three events A, B, and C, it becomes: P(A or B or C) = P(A) + P(B) + P(C) - P(A and B) - P(A and C) - P(B and C) + P(A and B and C) 2. Special Case of Addition: When two or more events will happen at the same time, and the events are mutually exclusive, then: P(X or Y) = P(X) + P(Y) 3. General Multiplication Rule: When two or more events will happen at the same time, and the events are dependent, then the general rule of multiplicative rule is used to find the joint probability:

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