can a mutually exclusive events be independent?
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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.
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A and B are independent if and only if P(A∩B)=P(A)P(B). In general, one cannot say whether two events are independent or not without knowing the actual probability distribution (though there are some exceptions).
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Mutually Exclusive Events. 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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Events are mutually exclusive if the occurrence of one event excludes the occurrence of the other(s). Mutually exclusive events cannot happen at the same time. ... This of course means mutually exclusive events are not independent, and independent events cannot be mutually exclusive.
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Mutually Exclusive Events Two events are mutually exclusive if they cannot occur at the same time. Another word that means mutually exclusive is disjoint.
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If A and B are independent events, then the events A and B' are also independent. ... From the Venn diagram, we see that the events A ∩ B and A ∩ B' are mutually exclusive and together they form the event A. A = ( A ∩ B) ∪ (A ∩ B'). Also, P(A) = P[(A ∩ B) ∪ (A ∩ B')].
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Mutually Exclusive Events. When two events, A and B, are mutually exclusive, it means that they cannot both occur at the same time. This would mean that the joint probability of A and B, as well as the conditional probabilities for A and B, are equal to 0.
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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) ... Therefore, A and B are not mutually exclusive.
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Two events are mutually exclusive if they can't both happen. Independent events are events where knowledge of the probability of one doesn't change the probability of the other.
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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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Mutually Exclusive Events: Definition and Examples. If two events are mutually exclusive, it means that they cannot occur at the same time. For example, the two possible outcomes of a coin flip are mutually exclusive; when you flip a coin, it cannot land both heads and tails simultaneously.
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Two events are independent if the result of the second event is not affected by the result of the first event. If A and B are independent events, the probability of both events occurring is the product of the probabilities of the individual events.
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The definition of being mutually exclusive (disjoint) means that it is impossible for two events to occur together. Given two events, A and B, they are mutually exclusive if (A П B) = 0. If these two events are mutually exclusive, they cannot be independent.
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When two events, A and B, are mutually exclusive, it means that they cannot both occur at the same time. This would mean that the joint probability of A and B, as well as the conditional probabilities for A and B, are equal to 0.
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If event A and event B cannot occur at the same time, then events A and B are said to be a) mutually exclusive.
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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. ... If two events are independent, they cannot be mutually exclusive.
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Mutually Exclusive and Collectively Exclusive Events: Two events are said to be mutually exclusive if the happening of one event prevents the other event from happening. That is, if they both cannot happen at the same time. Two events are collectively exhaustive if at least one of the events must occur.