if events a and b are independent what must be true quizlet?
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some outcome must occur on every trial, the sum of the probabilities for all possible outcomes must be exactly 1. ... 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) = P(A)P(B).
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If A, B, and C are mutually exclusive independent and exhaustive events, what is the probability that they occur simultaneously? ANSWER: Zero. A set of two or more events are said to be mutually exclusive if and only if it is impossible for the events to occur together.
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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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Independence. Two events A and B are called independent if P(A|B)=P(A), i.e., if conditioning on one does not effect the probability of the other.
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Product rule for independent events If A and B are independent, P(AB)=P(A)P(B) (because P(A|B)=P(A) for independent events). (Example: If A and B are independent and P(A)=.
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If A and B are independent events, then the events A and B' are also independent. Proof: The events A and B are independent, so, P(A ∩ B)
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To test whether two events A and B are independent, calculate P(A), P(B), and P(A ∩ B), and then check whether P(A ∩ B) equals P(A)P(B). If they are equal, A and B are independent; if not, they are dependent.
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Event that can't occur simultaneously are mutually exclusive. ... If events are independent outcome of one does not affect other event.Eg. 2 different events of tossing two coins are independent as outcome of one does not affect other.
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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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What is the difference between independent and dependent​ events? Two events are independent when the occurrence of one event does not affect the probability of the occurrence of the other event. Two events are dependent when the occurrence of one event affects the probability of the occurrence of the other event.
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According to the definition of independent events, A and B∪C are independent if and only if P(A∩(B∪C))=P(A)P(B∪C). Since A and B and A and C are independent, I know that P(A∩B)=P(A)P(B)andP(A∩C)=P(A)P(C).
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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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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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1 Expert Answer This argument shows that if two events are independent, then each event is independent of the complement of the other. Therefore A' and B' are also independent events.
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An independent event states that an event that has no connection to another event chances of happening or in other word, the events has no effect on probability of another event occurring. Given: A and B are independent events.
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A and B are two events. If A and B are independent, then the probability that events A and B both occur is: p(A and B) = p(A) x p(B).
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Mutually exclusive events are those that cannot happen simultaneously, whereas independent events are those whose probabilities do not affect one another.