decide if the events a and b are mutually exclusive?
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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. For example, suppose the sample space S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
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In other words, they are mutually exclusive. Put in formal terms, events A and B are disjoint if their intersection is zero: P(A∩B) = 0. ... Another way of looking at disjoint events are that they have no outcomes in common.
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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) ... Therefore, A and C are mutually exclusive.
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If two events are mutually exclusive, they cannot both occur in the same trial: the probability of their intersection is zero. The probability of their union is the sum of their probabilities.
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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)
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In general, two events A and B are called mutually exclusive events if the occurrence of any one of them excludes the occurrence of the other event, i.e., if they can not occur simultaneously. In this case the sets A and B are disjoint.
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Yes, two events with nonzero probabilities can be both independent and mutually exclusive when their probabilities are equal.
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Mutually Exclusive Events 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. 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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They are mutually exclusive if and only if P(X∩Y)=0. ... If the events are independent, then P(X)P(Y)=P(X∩Y)>0, which would imply that they are not mutually exclusive! In other words, the events cannot be both independent and mutually exclusive if both of their probabilities are greater than 0.
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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 The probability of A and B both occurring is 0 because they can't occur at the same time. If two events are mutually exclusive, then the probability of one or the other occurring is ...
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The one sentence summary: If A and B are mutually exclusive events, then they are independent if and only if P(A) = 0 or P(B) = 0.
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Answer and Explanation: If a and b are mutually exclusive events, P(a) = 0.1, and P(b) = 0.3, then P(a or b) = 0.4.
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If events A and B are mutually exclusive, then the probability of A or B is simply: p(A or B) = p(A) + p(B).
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If the outcome of event A is not affected by event B, then events A and B are said to be a) mutually exclusive. ... If event A and event B cannot occur at the same time, then events A and B are said to be a) mutually exclusive. b) independent. c) collectively exhaustive.
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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')].