events a and b are independent if and only if?
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Independent Events: 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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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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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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Events are dependent if the outcome of one event affects the outcome of another. ... 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).
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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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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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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.
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P(A and B) = 0. Therefore, we see that a mutually exclusive pair of nontrivial events are also necessarily dependent events. This makes sense because if A and B are mutually exclusive, then if A occurs, then B cannot also occur; and vice versa.
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There's a couple of different formulas, depending on if you have dependent events or independent events. Formula for the probability of A and B (independent events): p(A and B) = p(A) * p(B). If the probability of one event doesn't affect the other, you have an independent event.
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Let A and B be independent events, and let A and C be independent events. ... 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).
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Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together.
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Definition: Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring. Some other examples of independent events are: Landing on heads after tossing a coin AND rolling a 5 on a single 6-sided die.
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Events are mutually exclusive if the occurrence of one event excludes the occurrence of the other(s). Mutually exclusive events cannot happen at the same time. ... Events are independent if the occurrence of one event does not influence (and is not influenced by) the occurrence of the other(s).
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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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If Events A and B are mutually exclusive, P(A ∩ B) = 0.
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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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Yes, two events with nonzero probabilities can be both independent and mutually exclusive when their probabilities are equal.