what are independent and dependent probability?
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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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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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Independent random samples are selected from two different sets of observations. If the data values of one random sample do not affect the data values of the other random sample, then the samples are said to be independent random samples.
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There are two types of variables, namely independent and dependent variables. The distinction is made on the basis of whether the variable determines the other variable or is determined by another variable. The independent variable is those variables whose value does not depend on any other variable.
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By the classical definition of probability, Probability = . Therefore, the events “male” and “0 activities” are independent.
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Probability of Two Events Occurring Together: Independent Just multiply the probability of the first event by the second. For example, if the probability of event A is 2/9 and the probability of event B is 3/9 then the probability of both events happening at the same time is (2/9)*(3/9) = 6/81 = 2/27.
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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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- 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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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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Probability, Odds and Random Chance. Probability is the likelihood or chance that something will happen. Probability is an estimate of the relative average frequency with which an event occurs in repeated independent trials.
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A and B are independent if and only if P(A∩B)=P(A)P(B). In general, one cannot say whether two events are independent or not without knowing the actual probability distribution (though there are some exceptions).
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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 are mutually exclusive if they can't both happen. Independent events are events where knowledge of the probability of one doesn't change the probability of the other.
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Consider two discrete random variables X and Y. ... Intuitively, two random variables X and Y are independent if knowing the value of one of them does not change the probabilities for the other one. In other words, if X and Y are independent, we can write P(Y=y|X=x)=P(Y=y), for all x,y.
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Independent vs Dependent Variables An independent variable is the variable that is changed or controlled in a scientific experiment to test the effects on the dependent variable. A dependent variable is the variable being tested and measured in a scientific experiment.
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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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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).