select the correct answer. if a and b are independent events which equation must be true?
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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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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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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. Choosing a marble from a jar AND landing on heads after tossing a coin.
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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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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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['A and B together is impossible: P(A and B) = 0.', 'A or B is the sum of A and B: P(A or B) = P(A) + P(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) .
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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) = P(A) P(B). From the Venn diagram, we see that the events A ∩ B and A ∩ B' are mutually exclusive and together they form the event A.
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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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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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we know if two events A and B are independents then this means that the probability of their intersection is equal to the product of the probabilities of the two single events A and B. Hence, since the probability of A or B (the probability of the union of these two events) is: P(A or 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.
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The probability of the intersection of Events A and B is denoted by P(A ∩ B). 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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Independent/Dependent Events. 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. P(A and B)=P(A)⋅P(B)
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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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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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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.