can two events be independent and mutually exclusive?
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Mutually exclusive events cannot happen at the same time. For example: when tossing a coin, the result can either be heads or tails but cannot be both. ... This of course means mutually exclusive events are not independent, and independent events cannot be mutually exclusive. (Events of measure zero excepted.)
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are called mutually exclusive. These are events that cannot occur at the same time. When two events, A and B, are mutually exclusive, the probability of A and B, P(A∩B) = 0.
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Two events A and B are said to be mutually non exclusive events if both the events A and B have atleast one common outcome between them. The events A and B cannot prevent the occurrence of one another so from here we can say that the events A and B have something common in them.
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Two events are mutually exclusive if they cannot occur at the same time. ... If two events are mutually exclusive, then the probability of either occurring is the sum of the probabilities of each occurring.
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Two events are mutually exclusive if they cannot occur at the same time. Another word that means mutually exclusive is disjoint. ... If two events are mutually exclusive, then the probability of either occurring is the sum of the probabilities of each occurring.
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Two Mutually Exclusive Events Two events are mutually exclusive if they cannot occur at the same time. The two sets E1 and E2 have no elements in common and their intersection is an empty set since they cannot occur at the same time.
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Two events are mutually exclusive if they cannot occur at the same time (i.e., they have no outcomes in common). In the Venn Diagram above, the probabilities of events A and B are represented by two disjoint sets (i.e., they have no elements in common).
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A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B) = 0.
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P(A and B) = 0. Therefore, we see that a mutually exclusive pair of nontrivial events are also necessarily dependent events. This makes sense because if A and B are mutually exclusive, then if A occurs, then B cannot also occur; and vice versa.
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Two events E anf F are mutually exclusive if they have no outcomes in common. To use the set theory language Two events E and F are mutually exclusive if the intersection of E and F is empty. An equivalent term is disjoint.
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Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. ... When events do not share outcomes, they are mutually exclusive of each other.
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Two events are mutually exclusive if they cannot occur at the same time. Another word that means mutually exclusive is disjoint. If two events are disjoint, then the probability of them both occurring at the same time is 0.
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Consider 2 events A and B which satisfy the condition that they both are mutually exclusive and independent (simultaneously). Thus, if we chose any 2 events such that at least one of them is guaranteed to not occur, then those two events will be both mutually exclusive and independent.
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The difference between mutually exclusive and independent events is: a mutually exclusive event can simply be defined as a situation when two events cannot occur at same time whereas independent event occurs when one event remains unaffected by the occurrence of the other event.
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Mutually exclusive If events A and B are mutually exclusive of each other then the events will never be independent of each other. ... If the events are independent of each other then the Venn diagram can be simplified.
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However the event that you get two heads is mutually exclusive to the event that you get two tails. Suppose two events have a non-zero chance of occurring. Then if the two events are mutually exclusive, they can not be independent. If two events are independent, they cannot be mutually exclusive.
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Mutually Exclusive Events Two events are mutually exclusive if they cannot occur at the same time. ... If two events are disjoint, then the probability of them both occurring at the same time is 0.