See also several of the entries under Distributions, Frequency Data, Proportions, and Clinical Research Calculators.

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Randomness and the Appearance of Pattern. As the Latin playwright Terence put it in his Phormio: "How often things occur by the merest chance."

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Binomial Probabilities, as calculated or estimated according to one or more of the following methods:

	»Exact binomial probabilities
	»Approximation via the normal distribution
	»Approximation via the Poisson distribution

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For Sequential Sampling: Pascal (Negative Binomial) Probabilities. For a situation in which independent binomial events are randomly sampled in sequence, this page will calculate (a) the probability that you will end up with exactly k instances of the outcome in question, with the final (k^th) instance occurring on trial N; and (b) the probability that you will have to sample at least N events before finding the k^th instance of the outcome.

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Bayes' Theorem:_T
  Conditional Probabilities_T
  Adjustment of Subjective Confidence_T
Using multiple applications of Bayes' theorem, the first of these pages will delineate the relationships that exist within an array of simple and conditional probabilities. The second page performs the same calculations for the situation where the several probabilities are constructed as indices of subjective confidence.

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Backward Probability Template. Specific application of Bayes' theorem (above). Given the population incidence of a certain disease, and the conditional probabilities of positive and negative test results, what are the probabilities for a particular test result of a true positive, true negative, false positive, and false negative? Adaptable to other kinds of conditional situations.
[See also: Clinical Research Calculators.]

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