if a and b are independent events p(a)=.4 and p(b)=.6 find?
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SOLUTION: if A and B are independent events P(a)=. 4 and P(B)=. 6 find P(A U B) P(A U B) = P(A) + P(B) - P(AB) = 0.4 + 0.6 - 0.24 = 0.76.
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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)
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Since P(B) > 0 and P(B|A) = 0, the requirement that an event be contained by A does affect the probability of B occurring, so A and B are not independent. Thus, if A and B are mutually exclusive, they are not independent. Mutual exclusiveness implies that the probability of intersection of the two events is 0.
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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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Suppose a variable X can take the values 1, 2, 3, or 4. The probability that X is equal to 2 or 3 is the sum of the two probabilities: P(X = 2 or X = 3) = P(X = 2) + P(X = 3) = 0.3 + 0.4 = 0.7. Similarly, the probability that X is greater than 1 is equal to 1 - P(X = 1) = 1 - 0.1 = 0.9, by the complement rule.
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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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Since the events A and B are independent, the probability of both A and B occurring is the product of their individual probabilities.
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If A and B are independent, P(exactly one of them occurs) = P(A) + P(B) — 2P(A)*P(B)
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If A and B are two events in a sample space S, then the conditional probability of A given B is defined as P(A|B)=P(A∩B)P(B), when P(B)>0.
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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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An outcome is in the event A OR B if the outcome is in A, is in B, or is in both A and B. Two events are mutually exclusive if the probability that they both happen at the same time is zero. If events A and B are mutually exclusive, then P(A AND B) = 0.
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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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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) = P(B ∩ A) = P(B) × P(A).
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If two events A and B are mutually exclusive, the events are called disjoint events. ... If the events A and B are not mutually exclusive, the probability is: (A or B) = p(A) + p(B) – p(A and B).
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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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Prove that if event A and event B are mutually exclusive with P(A)≠0 and P(B)≠0, then A and B are always dependent. ... Since A and B are mutually exclusive, we know that P(A and B)=0. Therefore P(A)×P(B)=0. For the product of two numbers to be zero, at least one of the two numbers must be zero.
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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)