In this case, the relevant numerical information – p (drunk), p (D – drunk), p (D – sober) – is presented with regard to natural frequencies in relation to a given reference class (see reference class problem). Empirical studies show that human conclusions are more consistent with the Bayes rule when information is presented in this way, which helps to overcome the neglect of lay people and experts.  As a result, organizations such as Cochrane Collaboration recommend using this type of format to communicate health statistics.  Teaching people to translate these types of Bayes argument problems into natural frequency formats is more effective than simply teaching them to insert probabilities (or percentages) into Bayes` sentence.  Graphic representations of natural frequencies have also been shown (for example. B icon tables) help people draw better conclusions.    Therefore, the probability that one of the drivers among the 1 -49.95 -50.95 positive results is really drunk is 1/50.95 ≈ 0.019627 .-displaystyle 1/50.95`ca. 0.019627` . In population B, only 20 people out of a total of 69 are actually infected with a positive result. The probability of becoming infected after saying you are infected is only 29% (20/20 -49) for a test that appears to be « 95% accurate ». It is particularly counter-intuitive to interpret a positive result in a test on a low-prevalence population after treating positive results from a high-prevalence population.  If the false positive rate of the test is greater than the proportion of the new population with the disease, then a test administrator whose experience has been derived from tests in a high-prevalence population may infer from experience that a positive test result is generally indicative of a positive reason, although there was a falsely positive probability. The forward rate agreement, abbreviated FRA, is one of the most widely used financial instruments in the world of finance.
It is concluded between two counterparties, over-the-counter. N (drunk ∩ D) indicates the number of drunk drivers and a positive result from the respiratory analyzer and N (D) the total number of cases with a positive blood alcohol level. The equivalence of this equation to the above equation is the result of axioms in the theory of probabilities that N (drunk ∩ D) – N × p (D – drunk) is × p (drunk). It is important that this equation is formally consistent with the Baye rule, but that it is not psychologically equivalent. The use of natural frequencies simplifies the conclusion, because the necessary mathematical intervention can be performed on natural numbers instead of normalized fractions (i.e. probabilities), because it makes the high number of positive misrepresentations more transparent and because natural frequencies have a « nested structure ».   Not all frequency formats facilitate Bavarian thinking.   Natural frequencies refer to frequency information from natural samples that retains basic tariff information (for example. B the number of drunk drivers taken from a random sample of drivers). This is different from the systematic levies for which base rates are set in advance (for example.
B in scientific experiments). In the latter case, it is not possible to deduce the probability of the rear probability (drunk -positive test) of the comparison of the number of drunk drivers and the positive test in relation to the total number of people obtaining a positive result from the respiratory analyzer, as the basic tariff information is not maintained and must be reintroduced explicitly with the Bayes rate. In this example, the error of the basic interest rate is so misleading, because there are many more non-terrorists than terrorists and the number of false positives (non-terrorists scanned as terrorists) is much greater than the actual number of terrorists. An example of the basic interest rate error is the false positive paradox.