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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 ...
Two events, A and B are said to be mutually exclusive or disjoint if the occurrence of one implies the non-occurrence of the other, i.e., their intersection is empty. This is a stronger condition than the probability of their intersection being zero. If A and B are disjoint events, then P(A ∪ B) = P(A) + P(B). This extends to a (finite or ...
If either event A or event B can occur but never both simultaneously, then they are called mutually exclusive events. If two events are mutually exclusive, then the probability of both occurring is denoted as () and = = If two events are mutually exclusive, then the probability of either occurring is denoted as () and = = + () = + = + ()
This is the same as saying that the probability of event {1,2,3,4,6} is 5/6. This event encompasses the possibility of any number except five being rolled. The mutually exclusive event {5} has a probability of 1/6, and the event {1,2,3,4,5,6} has a probability of 1, that is, absolute certainty.
The red oval is the event that a number is odd, and the blue oval is the event that a number is prime. A sample space can be represented visually by a rectangle, with the outcomes of the sample space denoted by points within the rectangle. The events may be represented by ovals, where the points enclosed within the oval make up the event. [12]
The MECE principle (mutually exclusive and collectively exhaustive) is a grouping principle for separating a set of items into subsets that are mutually exclusive (ME) and collectively exhaustive (CE). [1]
Another example of events being collectively exhaustive and mutually exclusive at same time are, event "even" (2,4 or 6) and event "odd" (1,3 or 5) in a random experiment of rolling a six-sided die. These both events are mutually exclusive because even and odd outcome can never occur at same time. The union of both "even" and "odd" events give ...
A random experiment that has exactly two (mutually exclusive) possible outcomes is known as a Bernoulli trial. [2] When an experiment is conducted, one (and only one) outcome results— although this outcome may be included in any number of events, all of which would be said to have occurred