if two events are not mutually exclusive p (a or b) = p(a) + p(b)?
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Non-Mutually Exclusive Events In events which aren't mutually exclusive, there is some overlap. When P(A) and P(B) are added, the probability of the intersection (and) is added twice. To compensate for that double addition, the intersection needs to be subtracted.
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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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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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Mutually Exclusive Events 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 disjoint, then the probability of them both occurring at the same time is 0.
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If A and B are independent, then the probability that events A and B both occur is: p(A and B) ... Two events must occur: a head on the first toss and a head on the second toss. Since the probability of each event is 1/2, the probability of both events is: 1/2 x 1/2 = 1/4.
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Two events A and B are independent if knowing that one occurs does not change the probability that the other occurs. If A and B are independent, P(A and B) ... For any two events A and B, P(A or B) = P(A) + P(B) - P(A and B).
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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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SOLUTION: if A and B are independent events P(a)=. 4 and P(B)=. 6 find P(A U B) P(A U B) = P(A) + P(B) - P(AB) = 0.4 + 0.6 - 0.24 = 0.76.
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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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Since P(B) > 0 and P(B|A) = 0, the requirement that an event be contained by A does affect the probability of B occurring, so A and B are not independent. Thus, if A and B are mutually exclusive, they are not independent. Mutual exclusiveness implies that the probability of intersection of the two events is 0.
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In the case of two mutually exclusive events A and B, each of which has non-zero probability, we have that P(A)P(B)≠0, but P(A∩B)=0, so the events cannot be independent.
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2 events are mutually exclusive when they cannot both occur simultaneously. 2 events are mutually inclusive when they can both occur simultaneously. The possible results of 1 trial of a probability experiment.
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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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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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Two events are mutually exclusive or disjoint if they cannot occur at the same time. ... If Events A and B are mutually exclusive, P(A ∩ B) = 0. The probability that Events A or B occur is the probability of the union of A and B.
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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.