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Many probability text books and articles in the field of probability theory derive the conditional probability solution through a formal application of Bayes' theorem — among them books by Gill [51] and Henze. [52] Use of the odds form of Bayes' theorem, often called Bayes' rule, makes such a derivation more transparent. [34] [53]
Proof by assertion – a proposition is repeatedly restated regardless of contradiction; sometimes confused with argument from repetition (argumentum ad infinitum, argumentum ad nauseam). Prosecutor's fallacy – a low probability of false matches does not mean a low probability of some false match being found. [43] [44]
The name "probabilistic argumentation" has been used to refer to a particular theory of reasoning that encompasses uncertainty and ignorance, combining probability theory and deductive logic (Haenni, Kohlas & Lehmann 2000). OpenPAS is an open-source implementation of such a probabilistic argumentation system.
Double counting is a fallacy in reasoning. An example of double counting is shown starting with the question: What is the probability of seeing at least one 5 when throwing a pair of dice? An erroneous argument goes as follows: The first die shows a 5 with probability 1/6, and the second die shows a 5 with probability 1/6; therefore, the ...
Historically, attempts to quantify probabilistic reasoning date back to antiquity. There was a particularly strong interest starting in the 12th century, with the work of the Scholastics, with the invention of the half-proof (so that two half-proofs are sufficient to prove guilt), the elucidation of moral certainty (sufficient certainty to act upon, but short of absolute certainty), the ...
Plausible reasoning can be tested, and by this means, confirmed or refuted. Probing into plausible reasoning in a dialogue is a way of testing it. Plausible reasoning admits of degrees by testing, but of a kind different from those the standard probability values and Bayesian rules used in Pascalian probability
Inductive reasoning asserts that the probability of a conclusion being correct is adequate evidence to support the argument. [ citation needed ] Inductive arguments are judged on the strength or weakness of an argument and an argument's strength is subjective to each participant based on preconceptions about the subject being discussed.
The Boy or Girl paradox surrounds a set of questions in probability theory, which are also known as The Two Child Problem, [1] Mr. Smith's Children [2] and the Mrs. Smith Problem. The initial formulation of the question dates back to at least 1959, when Martin Gardner featured it in his October 1959 "Mathematical Games column" in Scientific ...
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