if events a and b are independent what must be true?
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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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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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One of the most important concepts in probability is that of independent events. Two events E and F are independent if the occurrence of event E does not affect the probability of event F.
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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 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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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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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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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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Independent Events Venn Diagram Theorem: If X and Y are independent events, then the events X and Y' are also independent. Proof: The events A and B are independent, so, P(X ∩ Y) = P(X) P(Y). From the Venn diagram, we see that the events X ∩ Y and X ∩ Y' are mutually exclusive and together they form the event X.
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Note that disjoint events and independent events are different. Events are considered disjoint if they never occur at the same time; these are also known as mutually exclusive events. Events are considered independent if they are unrelated. Two events that do not occur at the same time.
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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 dependent events, then the probability of A happening AND the probability of B happening, given A, is P(A) × P(B after A).', 'P(A and B) = P(A) × P(B after A)', 'then P(A and B) = P(A) × P(B | A)', 'Example:', 'Example:', 'Solution:']
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It is possible for two mutually exclusive events to be independent. The Multiplication Rule states that for any two events, P (E intersect F)(E ∩ F) = P(E|F) * P(F). Two events, E and F, are independent if P (E|F) = P(F|E) = P (F|E).
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By the classical definition of probability, Probability = . Therefore, the events “male” and “0 activities” are independent.
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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 events A and B are independent, and the probability that event A occurs is 83%, what must be true? The probability that event A occurs, given that event B occurs, is 83%.
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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) = p(A) x p(B). In other words, the probability of A and B both occurring is the product of the probability of A and the probability of B.