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Topic: Event probability theory

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	Probability space - Wikipédia
		In mathematics, a probability space is a set S, together with a σ-algebra X on S and a measure P on that σ-algebra such that P(S) = 1.
		The measure P is called the probability measure, and P(E) is the probability of the event E.
		The above is a compact form of stating the probability axioms.
	su.wikipedia.org /wiki/Probability_space (100 words)

	Event - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-07)
		An event can be significant - such as a major football match or an earthquake - or it can be insignificant - such as one raindrop making a ripple on a pond during a storm.
		The likelihood of an event being significant is approximated by Weinberg's Law of Twins.
		In probability a possible outcome of an experiment is called an elementary event, while a set of those (a subset of all) is called simply an event (see event (probability theory)).
	www.bexley.us /project/wikipedia/index.php/Events (422 words)

	Event (probability theory) - Wikipedia, the free encyclopedia
		In probability theory, an event is a set of outcomes (a subset of the sample space) to which a probability is assigned.
		Venn diagrams are particularly useful for representing events because the probability of the event can be identified with the ratio of the area of the event and the area of the sample space.
		In the measure-theoretic description of probability spaces, an event may be defined as an element of the σ-algebra on the sample space.
	en.wikipedia.org /wiki/Event_(probability_theory) (353 words)

	Probability - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-11-07)
		probability is taken as a primitive (that is, not further analyzed) and the emphasis is on constructing a consistent assignment of probability values to propositions.
		Probabilities are equivalently expressed as odds, which is the ratio of the probability of one event to the probability of all other events.
		Governments typically apply probability methods in environment regulation where it is called "pathway analysis", and are often measuring well-being using methods that are stochastic in nature, and choosing projects to undertake based on their perceived probable effect on the population as a whole, statistically.
	encyclopedia.worldsearch.com /probability.htm (2609 words)

	Introduction to Probability Theory (Site not responding. Last check: 2007-11-07)
		Probability: Probability is a numerical measure of the likelihood of an event relative to a set of alternative events.
		Let A be the event of rolling a 3, 4 or 6 (A = {3, 4, 6}) and B be the event of rolling a 2, 3 or 5 (B = {2, 3, 5}).
		Conditional probability of two events, A and B, is defined as the probability of one of the events occurring knowing that the other event has already occurred.
	www.weibull.com /hotwire/issue25/hottopics25.htm (1000 words)

	Probability - Open Encyclopedia (Site not responding. Last check: 2007-11-07)
		As with the theory of mechanics which assigns precise definitions to such everyday terms as work and force, so the theory of probability attempts to quantify the notion of probable.
		In Kolmogorov's formulation, sets are interpreted as events and probability itself as a measure on a class of sets.
		In Cox's formulation, probability is taken as a primitive (that is, not further analyzed) and the emphasis is on constructing a consistent assignment of probability values to propositions.
	open-encyclopedia.com /Probability (2628 words)

	Elementary event - Wikipedia, the free encyclopedia
		In probability theory, an elementary event or atomic event is a subset of a sample space that contains only one element.
		This example shows that a continuous probability distribution is not determined by the probabilities assigned to atomic events, since all of those are zero.
		Under the measure-theoretic definition of a probability space, the probability of an elementary event need not even be defined, since mathematicians distinguish between the sample space S and the events of interest, defined by the elements of a σ-algebra on S.
	en.wikipedia.org /?title=Elementary_event (321 words)

	History of Science: Origins of Modern Probability Theory (Site not responding. Last check: 2007-11-07)
		Probability, as the concept is most commonly understood in everyday language, is a mathematical expression of the relationship between a particular outcome of an event and total number of possible outcomes.
		Bernoulli interpreted probability as a state of mind rather than as a state of the world (for, in line with standard beliefs of the time, there was no randomness in the world of nature: "All things which exist or are acted upon under the sun--past, present, or future things--always have the greatest certainty") (5).
		As a mental state, probability, in his definition, "is a degree of certainty and differs from it as a part from the whole." The application of this definition marked a shift away from expectations to probabilities and from equiprobable outcomes to measures of certainty.
	www.mala.bc.ca /~johnstoi/darwin/sect4.htm (9704 words)

	Elementary event - Wikipedia, the free encyclopedia
		However, elementary events are often written as elements rather than sets for simplicity, where this is unambiguous.
		Elementary events may have probabilities that are strictly positive, zero, undefined, or any combination thereof.
		For instance, any discrete probability distribution is determined by the probabilities it assigns to what may be called elementary events.
	en.wikipedia.org /wiki/Elementary_event (321 words)

	All Elementary Mathematics - Study Guide - Probability - Events...
		An event in probability theory is any fact, which may occur as a result of an experiment with a random outcome or may not.
		An event can consist of one or several elementary events, for example, an appearance of two aces one after the other at taking a card out of a pack, or an appearance of the same number at triple throwing of a die.
		Such event at throwing of a die is a fall of the die on one of its faces.
	www.bymath.com /studyguide/prob/sec/prob1.htm (512 words)

	Event (probability theory): Definition and Links by Encyclopedian.com - All about Event (probability theory) (Site not responding. Last check: 2007-11-07)
		Mathematically, an event is defined as an element of the σ-algebra of the probability space.
		For example, if we assemble a deck of 52 playing cards and two jokers, each individual card represents an elementary event in a 54-element sample set, but subsets of the sample set (regardless of how many elementary events they contain) are called simply "events".
		Events from this sample set include "King" (a set 4 elementary events), "Spade" (13 elementary events), and "Face card" (12 elementary events).
	www.encyclopedian.com /pr/Probability---Event.html (136 words)

	Probability theory - FreeEncyclopedia (Site not responding. Last check: 2007-11-07)
		Probability theory is the mathematical study of probability.
		The sum of the probabilities of all the elementary events is one.
		, the probability of either or both is given by the sum of the probabilities of the two events minus the probability of both.
	openproxy.ath.cx /pr/Probability_theory.html (177 words)

	Event article - Event duration football music concert information processing properties - What-Means.com (Site not responding. Last check: 2007-11-07)
		In common language, an event is something that happens (changes), in particular something special of limited duration, for example a major football match or pop music concert.
		An event is an outcome, result, reference or single point of focus.
		In philosophy, one might want to distinguish between physical events, mental events, and brain events.
	www.what-means.com /encyclopedia/Event (363 words)

	Statistics Glossary - probability
		Probability is conventionally expressed on a scale from 0 to 1; a rare event has a probability close to 0, a very common event has a probability close to 1.
		Like all probabilities, a subjective probability is conventionally expressed on a scale from 0 to 1; a rare event has a subjective probability close to 0, a very common event has a subjective probability close to 1.
		In probability theory we say that two events, A and B, are independent if the probability that they both occur is equal to the product of the probabilities of the two individual events, i.e.
	www.stats.gla.ac.uk /steps/glossary/probability.html (1632 words)

	Probability Theory - The Laymans guide to probability (Site not responding. Last check: 2007-11-07)
		The probability of throwing a double three with two dice is the result of throwing three with the first die and three with the second die.
		The two events are independent, since whatever happens to the first die cannot affect the throw of the second, the probabilities are therefore multiplied, and remain 1/36th.
		For example, The probability of throwing a 1 on a die is 1/6 therefore the probability of a 'non-1' is (1-1/6) which equals 5/6.
	www.probabilitytheory.info - !http: //www.peterwebb.co.uk/probability.htm (6661 words)

	probability theory -- Encyclopædia Britannica (Site not responding. Last check: 2007-11-07)
		The ligand field theory deals with the origins and consequences of metal– ligand interactions as a means of...
		His original contributions to the fields of probability theory and topology have had a significant impact on modern physics, chemistry, biology, and cybernetics.
		Jakob (1654–1705), a professor of mathematics at the University of Basel, is best known for his work on the theory of probability and his principles of the calculus of variation.
	www.britannica.com /eb/article-9109439 (931 words)

	Quantum Logic and Probability Theory
		It is uncontroversial (though remarkable) that the formal apparatus of quantum mechanics reduces neatly to a generalization of classical probability in which the role played by a Boolean algebra of events in the latter is taken over by the "quantum logic" of projection operators on a Hilbert space.
		Mackey presents a sequence of six axioms, framing a very conservative generalized probability theory, that underwrite the construction of a ‘logic’ of experimental propositions, or, in his terminology, ‘questions’, having the structure of a sigma-orthomodular poset.
		In classical probability theory (and especially in classical statistics) one usually focuses, not on the set of all possible probability weights, but on some designated subset of these (e.g., those belonging to a given family of distributions).
	plato.stanford.edu /entries/qt-quantlog (7961 words)

	The Poisson process (from probability theory) -- Encyclopædia Britannica
		In genetics, for example, probability is used to estimate the likelihood for brown-eyed parents to produce a blue-eyed child (see Heredity).
		in mathematics and mechanics, theory that studies systems behaving unpredictably and randomly despite their seeming simplicity and fact that forces involved are supposedly governed by well-understood physical laws; applications of theory are diverse, including study of turbulent flow of fluids, irregularities in heartbeat, traffic jams, population dynamics, chemical...
		class of quantum field theory used to describe subatomic particles and their associated relativistic quantum fields; all measurable physical properties remain unchanged when certain mathematical symmetry operations are performed on the quantum fields; believed that the final unification of the four fundamental interactions—gravitational, electromagnetic, strong, and...
	www.britannica.com /eb/article-32788?tocId=32788 (862 words)

	Foundations of Probability Theory: Basic Definitions (Site not responding. Last check: 2007-11-07)
		The basis of probability theory is a set of events - sample space - and a systematic set of numbers - probabilities - assigned to each event.
		The consistent set of probabilities Pr[·] assigned to events are known as the a priori probabilities.
		This calculation is known as the conditional probability of A given B and is denoted by Pr[ A,,
	cnx.rice.edu /content/m11245/latest (364 words)

	Elementary event (Site not responding. Last check: 2007-11-07)
		In probability theory, an elementary event (probability theory)event''' or '''atomic event is a subset of a sample space/ that contains only one element.
		For instance, any discrete random variablediscrete probability distribution is determined by the Probabilityprobabilities it assigns to what may be called elementary events.
		Under the measure theorymeasure-theoretic definition of a probability space, the probability of an elementary event need not even be defined, since mathematicians distinguish between the sample space ''S'' and the events of interest, defined by the elements of a sigma-algebraσ-algebra/ on ''S''.
	www.infothis.com /find/Elementary_event (564 words)

	Math Forum: Ask Dr. Math FAQ: The Birthday Problem
		To find the probability that both people have this birthday, we have to multiply their separate probabilities.
		To solve the birthday problem, we need to use one of the basic rules of probability: the sum of the probability that an event will happen and the probability that the event won't happen is always 1.
		We know that the probability of finding at least two people with the same birthday is 1 minus the probability that everybody has a different birthday, and we know how to find the probability that everybody has a different birthday for any number of people.
	mathforum.org /dr.math/faq/faq.birthdayprob.html (839 words)

	60: Probability theory and stochastic processes
		Probability theory is simply enumerative combinatorial analysis when applied to finite sets; thus the techniques and results resemble those of discrete mathematics.
		Probability concepts are applied across mathematics when considering random structures, and in particular lead to good algorithms in some settings even in pure mathematics.
		Probability questions given a finite sample space are usually "just" a lot of counting, and so are included with combinatorics.
	www.math.niu.edu /~rusin/known-math/index/60-XX.html (865 words)

	ipedia.com: Event (probability theory) Article (Site not responding. Last check: 2007-11-07)
		In probability theory, an event is a set of outcomes to which a probability is assigned.
		Typically, any subset of the sample space is an event, but when defining a probability space it is possible to...
		By the ratio of their areas, the probability of B is approximately 0.3.
	www.ipedia.com /event__probability_theory_.html (371 words)

	Probability Theory
		The probability of an event A out of a set of potential outcomes S is a number denoted as P[A].
		A Bernoulli Trial is a random process (like a coin toss) where the outcome event A (e.g.
		The probability of k successes in n trials is given by the Bernoulli probability law:
	www.cc.gatech.edu /classes/AY2002/cs4251_fall/references/PT.htm (91 words)

	Gambling Formula: Probability Theory, Mathematics, Chance
		the probability of getting one point face when rolling a die is '1 in 6' or p = 1/6; the probability of getting one roulette number is '1 in 38' or p = 1/38.
		If the probability is 1/N and we repeat the event N times, the degree of certainty is {1 — (1/e)}, when N tends to infinity.
		It means that it takes 1 event (coin toss, that is) in order to have a 50-50 chance (or degree of certainty of 50%) that either heads or tails will come out.
	www.saliu.com /Saliu2.htm (2844 words)

	Poker Probability (Site not responding. Last check: 2007-11-07)
		In poker, the probability of each type of 5 card hand can be computed by calculating the proportion of hands of that type among all possible hands.
		Here, the probability is the frequency of the hand divided by the total number of 5 card hands, and the odds are defined by (1/p) - 1 : 1, where p is the probability.
		The reader should be familiar with the basic properties of the binomial coefficients and their interpretation as the number of ways of choosing elements from a given set.
	www.texasholdempokerpro.com /probability.shtml (181 words)

	Probability Theory (Site not responding. Last check: 2007-11-07)
		, the probability of the desired outcomes is:
		Join Probability: The probability of the desired outcomes is the sum of the probability of each event resulting in a desired outcome.
		Both variance and standard deviation are used to describe the spread of a distribution.
	www.efunda.com /math/probability/probability.cfm (206 words)

	Probability Theory - Pascal's triangle - Combinations and Permutations
		Probability Theory - Pascal's triangle - Combinations and Permutations
		The problem with wheels of course is they can generate very efficient covering combinations but they actually make no difference to your chance of winning a random event.
		However I have put them to use in a number of situations and they are interesting to study but you will need a good grounding in combinations and permutations before you get to grips with them fully.
	www.probabilitytheory.info /topics/pascal_combinations_permutations.htm (1237 words)

	Probability Learning, Event-Splitting Effects and the Economic Theory of Choice ewp-exp/9702001 (Site not responding. Last check: 2007-11-07)
		Probability Learning, Event-Splitting Effects and the Economic Theory of Choice ewp-exp/9702001
		It is also suggested and empirically substantiated that stripped-down prospect theory will accurately predict ESEs in some decision making tasks, but will not perform well in others.
		This contention, it is argued, is indicative of fundamental descriptive shortcomings in the economic conception of choice under uncertainty and may entail implications beyond the direct concerns of the paper.
	econwpa.wustl.edu /eprints/exp/papers/9702/9702001.abs (182 words)

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