if a and b are independent events then show that ac and b are also independent?
16993
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) = P(A) P(B).
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- If A and B are independent, then having information on A does not tell us anything about B. - If A and B are disjoint, then knowing that A occurs tells us that B cannot occur. - Disjoint (mutually exclusive) events are always dependent since if one event occurs we know the other one cannot.
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Mutually exclusive If events A and B are mutually exclusive of each other then the events will never be independent of each other. ... If the events are independent of each other then the Venn diagram can be simplified.
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The probability that Events A or B occur is the probability of the union of A and B. The probability of the union of Events A and B is denoted by P(A ∪ B) .
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Therefore, we see that a mutually exclusive pair of nontrivial events are also necessarily dependent events. ... 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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If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A U B)=? We know the following formula for the probability of 2 events: P(A U B) = P(A) + P(B) - P(A intersection B) We're told A and B are independent, which makes P(A intersection B)
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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. The probability of the union of Events A and B is denoted by P(A ∪ B) .
605629
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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Independent Events If events are independent, then the probability of them both occurring is the product of the probabilities of each occurring.
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Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur. If whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.
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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.
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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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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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This makes sense because if A and B are mutually exclusive, then if A occurs, then B cannot also occur; and vice versa. ... Then if the two events are mutually exclusive, they can not be independent. If two events are independent, they cannot be mutually exclusive.
191647
When A and B are independent, the intersection of two events has P(A ∩ B) = P(A) × P(B). P(A ∩ B) = 0, and thus P(A ∪ B)
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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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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)=.