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P(A|B) may or may not be equal to P(A), i.e., the unconditional probability or absolute probability of A. If P(A|B) = P(A), then events A and B are said to be independent: in such a case, knowledge about either event does not alter the likelihood of each other. P(A|B) (the conditional probability of A given B) typically differs from P(B|A).
Then the unconditional probability that = is 3/6 = 1/2 (since there are six possible rolls of the dice, of which three are even), whereas the probability that = conditional on = is 1/3 (since there are three possible prime number rolls—2, 3, and 5—of which one is even).
In the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions.
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Math: the four-letter word you can say on TV yet so reviled that people go great lengths to avoid it, even when they know doing so puts their financial well-being in peril. Wait! Don't click away.
This article is written for those who want to get better at using price to earnings ratios (P/E ratios). To keep it...
P( at least one estimation is bad) = 0.05 ≤ P( A 1 is bad) + P( A 2 is bad) + P( A 3 is bad) + P( A 4 is bad) + P( A 5 is bad) One way is to make each of them equal to 0.05/5 = 0.01, that is 1%. In other words, you have to guarantee each estimate good to 99%( for example, by constructing a 99% confidence interval) to make sure the total ...
P (A), the prior, is the initial degree of belief in A. P (A | B), the posterior, is the degree of belief after incorporating news that B is true. the quotient P(B | A) / P(B) represents the support B provides for A. For more on the application of Bayes' theorem under the Bayesian interpretation of probability, see Bayesian inference.