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Boy Or Girl Paradox
The Boy or Girl paradox surrounds a set of questions in probability theory, which are also known as The Two Child Problem, Mr. Smith's Children 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 American''. He titled it The Two Children Problem, and phrased the paradox as follows: *Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls? *Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys? Gardner initially gave the answers and , respectively, but later acknowledged that the second question was ambiguous. Its answer could be , depending on the procedure by which the information "at least one of them is a boy" was obtained. The ambiguity, depending on the exact wording and possible assumptions, was confirmed by Maya Bar-H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms of probability, axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure (mathematics), measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event (probability theory), event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of determinism, non-deterministic or uncertain processes or measured Quantity, quantities that may either be single occurrences or evolve over time in a random fashion). Although it is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model (abstract)
The term conceptual model refers to any model that is formed after a wikt:concept#Noun, conceptualization or generalization process. Conceptual models are often abstractions of things in the real world, whether physical or social. Semantics, Semantic studies are relevant to various stages of process of concept formation, concept formation. Semantics is fundamentally a study of concepts, the meaning that thinking beings give to various elements of their experience. Overview Concept models and conceptual models The value of a conceptual model is usually directly proportional to how well it corresponds to a past, present, future, actual or potential state of affairs. A concept model (a model of a concept) is quite different because in order to be a good model it need not have this real world correspondence. In artificial intelligence, conceptual models and conceptual graphs are used for building expert systems and knowledge-based systems; here the analysts are concerned to repres ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Paradoxes
This list includes well known paradoxes, grouped thematically. The grouping is approximate, as paradoxes may fit into more than one category. This list collects only scenarios that have been called a paradox by at least one source and have their own article in this encyclopedia. These paradoxes may be due to fallacious reasoning (falsidical), or an unintuitive solution (Veridical paradox, veridical). The term ''paradox'' is often used to describe a counter-intuitive result. However, some of these paradoxes qualify to fit into the mainstream viewpoint of a paradox, which is a self-contradictory result gained even while properly applying accepted ways of reasoning. These paradoxes, often called ''antinomy,'' point out genuine problems in our understanding of the ideas of truth and Definite description, description. Logic * : The supposition that, "if one of two simultaneous assumptions leads to a contradiction, the other assumption is also disproved" leads to paradoxical conseq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two Envelopes Problem
The two envelopes problem, also known as the exchange paradox, is a paradox in probability theory. It is of special interest in decision theory and for the Bayesian interpretation of probability theory. It is a variant of an older problem known as the necktie paradox. The problem is typically introduced by formulating a hypothetical challenge like the following example: Since the situation is symmetric, it seems obvious that there is no point in switching envelopes. On the other hand, a simple calculation using expected values suggests the opposite conclusion, that it is always beneficial to swap envelopes, since the person stands to gain twice as much money if they switch, while the only risk is halving what they currently have. Introduction Problem A person is given two indistinguishable envelopes, each of which contains a sum of money. One envelope contains twice as much as the other. The person may pick one envelope and keep whatever amount it contains. They pick one env ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sleeping Beauty Problem
The Sleeping Beauty problem, also known as the Sleeping Beauty paradox, is a puzzle in decision theory in which an ideally rational Epistemology, epistemic agent is told she will be awoken from sleep either once or twice according to the toss of a coin. Each time she will have no memory of whether she has been awoken before, and is asked what her degree of belief that “the outcome of the coin toss is Heads” ought to be when she is first awakened. History The problem was originally formulated in unpublished work in the mid-1980s by Arnold Zuboff (the work was later published as "One Self: The Logic of Experience") followed by a paper by Adam Elga. A formal analysis of the problem of belief formation in decision problems with imperfect recall was provided first by Michele Piccione and Ariel Rubinstein in their paper: "On the Interpretation of Decision Problems with Imperfect Recall" where the "paradox of the absent minded driver" was first introduced and the Sleeping Beauty pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Necktie Paradox
The two envelopes problem, also known as the exchange paradox, is a paradox in probability theory. It is of special interest in decision theory and for the Bayesian interpretation of probability theory. It is a variant of an older problem known as the necktie paradox. The problem is typically introduced by formulating a hypothetical challenge like the following example: Since the situation is symmetric, it seems obvious that there is no point in switching envelopes. On the other hand, a simple calculation using expected values suggests the opposite conclusion, that it is always beneficial to swap envelopes, since the person stands to gain twice as much money if they switch, while the only risk is halving what they currently have. Introduction Problem A person is given two indistinguishable envelopes, each of which contains a sum of money. One envelope contains twice as much as the other. The person may pick one envelope and keep whatever amount it contains. They pick one env ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bertrand Paradox (probability)
The Bertrand paradox is a problem within the classical interpretation of probability theory. Joseph Bertrand introduced it in his work ''Calcul des probabilités'' (1889) as an example to show that the principle of indifference may not produce definite, well-defined results for probabilities if it is applied uncritically when the domain of possibilities is infinite. Bertrand's formulation of the problem The Bertrand paradox is generally presented as follows: Consider an equilateral triangle that is inscribed in a circle. Suppose a chord of the circle is chosen at random. What is the probability that the chord is longer than a side of the triangle? Bertrand gave three arguments (each using the principle of indifference), all apparently valid yet yielding different results: # The "random endpoints" method: Choose two random points on the circumference of the circle and draw the chord joining them. To calculate the probability in question imagine the triangle rotated so its vert ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heuristics
A heuristic or heuristic technique (''problem solving'', '' mental shortcut'', ''rule of thumb'') is any approach to problem solving that employs a pragmatic method that is not fully optimized, perfected, or rationalized, but is nevertheless "good enough" as an approximation or attribute substitution. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of making a decision. Context Gigerenzer & Gaissmaier (2011) state that sub-sets of ''strategy'' include heuristics, regression analysis, and Bayesian inference. Heuristics are strategies based on rules to generate optimal decisions, like the anchoring effect and utility maximization problem. These strategies depend on using readily accessible, though loosely applicable, information to control problem solving in human beings, machines and abstrac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bertrand's Box Paradox
Bertrand's box paradox is a Paradox#Quine's_classification, veridical paradox in elementary probability theory. It was first posed by Joseph Bertrand in his 1889 work Calcul des Probabilités'. There are three boxes: # a box containing two gold coins, # a box containing two silver coins, # a box containing one gold coin and one silver coin. A coin withdrawn at random from one of the three boxes happens to be a gold. What is the probability the other coin from the same box will also be a gold coin? A veridical paradox is a paradox whose correct solution seems to be counterintuitive. It may seem intuitive that the probability that the remaining coin is gold should be , but the probability is actually . Bertrand showed that if were correct, it would result in a contradiction, so cannot be correct. This simple but counterintuitive puzzle is used as a standard example in teaching probability theory. The solution illustrates some basic principles, including the Kolmogorov axioms. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monty Hall Problem
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show ''Let's Make a Deal'' and named after its original host, Monty Hall. The problem was originally posed (and solved) in a letter by Steve Selvin to the ''The American Statistician, American Statistician'' in 1975. It became famous as a question from reader Craig F. Whitaker's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in ''Parade (magazine), Parade'' magazine in 1990: Savant's response was that the contestant should switch to the other door. By the standard assumptions, the switching strategy has a probability of winning the car, while the strategy of keeping the initial choice has only a probability. When the player first makes their choice, there is a chance that the car is behind one of the doors not chosen. This probability does not change after the host reveals a goat behind one of the unchosen doors. When the host provides i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Experimental Psychology
The ''Journal of Experimental Psychology'' was a bimonthly peer-reviewed academic journal published by American Psychological Association. Established in 1916, it became the association's largest and most prestigious journal by the mid-1970s, when dissatisfaction with publication lag led the organization to restructure the journal. Beginning in 1975, it was split into four independently edited and distributed successor journals, with an additional successor journal being added in 1995. History The first issue was published by the Psychological Review Company, Princeton, New Jersey The Municipality of Princeton is a Borough (New Jersey), borough in Mercer County, New Jersey, United States. It was established on January 1, 2013, through the consolidation of the Borough of Princeton, New Jersey, Borough of Princeton and Pri .... The following successor journals are currently published: *'' Journal of Experimental Psychology: General'' *'' Journal of Experimental Psychology: Lea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marilyn Vos Savant
Marilyn vos Savant ( ; born Marilyn Mach; August 11, 1946) is an American magazine columnist who has the highest recorded intelligence quotient (IQ) in the ''Guinness Book of Records'', a competitive category the publication has since retired. Since 1986, she has written "Ask Marilyn", a '' Parade'' magazine Sunday column wherein she solves puzzles and answers questions on various subjects, and which popularized the Monty Hall problem in 1990. Biography Marilyn vos Savant was born Marilyn Mach on August 11, 1946, in St. Louis, Missouri, to parents Joseph Mach and Marina vos Savant. Savant says one should keep premarital surnames, with sons taking their father's and daughters their mother's. The word ''savant'', meaning someone of learning, appears twice in her family: her grandmother's name was Savant; her grandfather's, vos Savant. She is of Italian, Czechoslovak, German, and Austrian ancestry, being descended from the physicist and philosopher Ernst Mach. She went to Mera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
