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In logic, two propositions and are mutually exclusive if it is not logically possible for them to be true at the same time; that is, () is a tautology. To say that more than two propositions are mutually exclusive, depending on the context, means either 1. "() () is a tautology" (it is not logically possible for more than one proposition to be true) or 2. "() is a tautology" (it is not ...
The events 1 and 6 are mutually exclusive but not collectively exhaustive. The events "even" (2,4 or 6) and "not-6" (1,2,3,4, or 5) are also collectively exhaustive but not mutually exclusive. In some forms of mutual exclusion only one event can ever occur, whether collectively exhaustive or not.
The law of total probability is [1] a theorem that states, in its discrete case, if {: =,,, …} is a finite or countably infinite set of mutually exclusive and collectively exhaustive events, then for any event
In probability theory, the craps principle is a theorem about event probabilities under repeated iid trials. Let and denote two mutually exclusive events which might occur on a given trial.
If events A 1, A 2, ..., are mutually exclusive and exhaustive, i.e., one of them is certain to occur but no two can occur together, we can determine the proportionality constant by using the fact that their probabilities must add up to one. For instance, for a given event A, the event A itself and its complement ¬A are
The worst of the pandemic appears to be behind us, and Americans are back to attending in-person events in droves. Going to a wedding or a dance party is one thing, but what about the Met Gala or ...
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
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