if a and b are independent events then prove that a' and b are also independent?
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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).
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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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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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Yes, two events with nonzero probabilities can be both independent and mutually exclusive when their probabilities are equal. ... No, two events with nonzero probabilities cannot be independent and mutually exclusive because independence is the complement of being mutually exclusive.
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Probability Rule Six (The Multiplication Rule for Independent Events): If A and B are two INDEPENDENT events, then P(A and B) = P(A) * P(B).
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If A and B are Independent 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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In the case of two mutually exclusive events A and B, each of which has non-zero probability, we have that P(A)P(B)≠0, but P(A∩B)=0, so the events cannot be independent.
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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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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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SOLUTION: suppose a and b are independent events what if p (a)=0.5 and p(b) =0.45 what is p( a n b) When the independent the product of the two is the joint probability. If it is p( a and b), it is 0.5*0.45=0.225.
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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. All you do is multiply the probability of one by the probability of another.
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The probability that Events A and B both occur is the probability of the intersection of A and B. 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.
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Events A and B are independent if: knowing whether A occured does not change the probability of B. Mathematically, can say in two equivalent ways: P(B|A) = P(B) P(A and B) ... Important to distinguish independence from mutually exclusive which would say B ∩ A is empty (cannot happen).
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1 Answer. Mutual independence: Every event is independent of any intersection of the other events. Pairwise independence: Any two events are independent.
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If events A and B are mutually exclusive, then the probability of A or B is simply: p(A or B) = p(A) + p(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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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.