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Fundamentals of Applied Probability
Published in Ephraim Suhir, Human-in-the-Loop, 2018
5. An opposite or complementary event of A is an event Ā of nonoccurrence of the event A. The domain Ā is the complement of the domain A with respect to the complete space Ω. As follows from the definition of the complementary event, A¯¯=A,Ω¯=∅,∅¯=Ω.
Robust disassembly line balancing with ambiguous task processing times
Published in International Journal of Production Research, 2020
Ming Liu, Xin Liu, Feng Chu, Feifeng Zheng, Chengbin Chu
For Constraint (1), i.e. , we first use Φ to denote the associated event , and to denote its complementary event (i.e. ). Accordingly, the considered joint chance constraint is equivalent to Naturally, we have Finally, we can have where denotes the supremum of the probability. Following Boole's inequality, we have
Representing uncertainty in natural hazard risk assessment with Dempster Shafer (Evidence) theory
Published in Sustainable and Resilient Infrastructure, 2019
Wendy Ballent, Ross B Corotis, Cristina Torres-Machi
Equation (1) requires that any information provided about element or set ‘A’ also provides contrary evidence about the complementary event or set ‘A’. In Probability Theory, uncertainty is represented by this single probability measure. If either the probability of an event or set or the probability of its negation (or complement) is known, the additivity requirement guarantees that the probabilities of both are known. In the case of evidence theory, one expert might be prepared to assign a certain degree of evidence (sometimes conveniently viewed as confidence or belief), for instance, that a particular structure has been rendered uninhabitable following an earthquake. As an example, let this event be designated A, and let this belief be 30%. Because there is a lot of uncertainty and unknown about the details of the building’s condition, this same expert might be prepared to assign a belief, confidence or evidence of 40% that the building is inhabitable, designated Ā. In this case the expert does not have 100% evidence (belief or confidence) of the status of the structure.
The impact of a game and simulation-based probability learning environment on the achievement and attitudes of prospective teachers
Published in International Journal of Mathematical Education in Science and Technology, 2022
In the concept test, the definitions of a total of 20 concepts were sought. These concepts were probability, experiment, sample space, event, output, complementary event, impossible event, certain event, random variable, random event, equally likely events, discrete event, dependent event, independent event, conditional probability, experimental probability, discrete random variable, continuous variable, and normal distribution.