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Equally Likely Outcomes
In probability theory, an outcome is a possible result of an experiment or trial. Each possible outcome of a particular experiment is unique, and different outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment). All of the possible outcomes of an experiment form the elements of a sample space. For the experiment where we flip a coin twice, the four possible ''outcomes'' that make up our ''sample space'' are (H, T), (T, H), (T, T) and (H, H), where "H" represents a "heads", and "T" represents a "tails". Outcomes should not be confused with ''events'', which are (or informally, "groups") of outcomes. For comparison, we could define an event to occur when "at least one 'heads'" is flipped in the experiment - that is, when the outcome contains at least one 'heads'. This event would contain all outcomes in the sample space except the element (T, T). Sets of outcomes: events Since individual outcomes may be of little practical interest, or becaus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory 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. Typically these axioms formalise probability in terms of a probability space, which assigns a 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. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prentice Hall
Prentice Hall was an American major educational publisher owned by Savvas Learning Company. Prentice Hall publishes print and digital content for the 6–12 and higher-education market, and distributes its technical titles through the Safari Books Online e-reference service. History On October 13, 1913, law professor Charles Gerstenberg and his student Richard Ettinger founded Prentice Hall. Gerstenberg and Ettinger took their mothers' maiden names, Prentice and Hall, to name their new company. Prentice Hall became known as a publisher of trade books by authors such as Norman Vincent Peale; elementary, secondary, and college textbooks; loose-leaf information services; and professional books. Prentice Hall acquired the training provider Deltak in 1979. Prentice Hall was acquired by Gulf+Western in 1984, and became part of that company's publishing division Simon & Schuster. S&S sold several Prentice Hall subsidiaries: Deltak and Resource Systems were sold to National Education ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dice
Dice (singular die or dice) are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random values, commonly as part of tabletop games, including dice games, board games, role-playing games, and games of chance. A traditional die is a cube with each of its six faces marked with a different number of dots ( pips) from one to six. When thrown or rolled, the die comes to rest showing a random integer from one to six on its upper surface, with each value being equally likely. Dice may also have polyhedral or irregular shapes, may have faces marked with numerals or symbols instead of pips and may have their numbers carved out from the material of the dice instead of marked on it. Loaded dice are designed to favor some results over others for cheating or entertainment. History Dice have been used since before recorded history, and it is uncertain where they originated. It is theorized that dice developed from the practice ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Card Marking
Card marking is the process of altering playing cards in a method only apparent to marker or conspirator, such as by bending or adding visible marks to a card. This allows different methods for card sharps to cheat or for magicians to perform magic tricks. To be effective, the distinguishing mark or marks must be visible on the obverse sides of the cards, which are normally uniform. Card marking is often used to cheat when gambling or for card tricks. Many casinos, particularly those in Las Vegas alter the decks of cards they sell to tourists – either by punching holes through the middle of cards or trimming their edges – to prevent cheaters from returning to the game tables after buying the cards and then slipping the favorable cards into their hands when playing. Marked cards can be used regardless of who shuffles and deals the cards. Some more sophisticated marked-cards scams involve additional manipulative skills to steer the cards into the correct positions once the des ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lottery
A lottery is a form of gambling that involves the drawing of numbers at random for a prize. Some governments outlaw lotteries, while others endorse it to the extent of organizing a national or state lottery. It is common to find some degree of regulation of lottery by governments. The most common regulation is prohibition of sale to minors, and vendors must be licensed to sell lottery tickets. Although lotteries were common in the United States and some other countries during the 19th century, by the beginning of the 20th century, most forms of gambling, including lotteries and sweepstakes, were illegal in the U.S. and most of Europe as well as many other countries. This remained so until well after World War II. In the 1960s, casinos and lotteries began to re-appear throughout the world as a means for governments to raise revenue without raising taxes. Lotteries come in many formats. For example, the prize can be a fixed amount of cash or goods. In this format, there is risk t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Playing Card
A playing card is a piece of specially prepared card stock, heavy paper, thin cardboard, plastic-coated paper, cotton-paper blend, or thin plastic that is marked with distinguishing motifs. Often the front (face) and back of each card has a finish to make handling easier. They are most commonly used for playing card games, and are also used in magic tricks, cardistry, card throwing, and card houses; cards may also be collected. Some patterns of Tarot playing card are also used for divination, although bespoke cards for this use are more common. Playing cards are typically palm-sized for convenient handling, and usually are sold together in a set as a deck of cards or pack of cards. The most common type of playing card in the West is the French-suited, standard 52-card pack, of which the most widespread design is the English pattern, followed by the Belgian-Genoese pattern. However, many countries use other, traditional types of playing card, including those that are German ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dice
Dice (singular die or dice) are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random values, commonly as part of tabletop games, including dice games, board games, role-playing games, and games of chance. A traditional die is a cube with each of its six faces marked with a different number of dots ( pips) from one to six. When thrown or rolled, the die comes to rest showing a random integer from one to six on its upper surface, with each value being equally likely. Dice may also have polyhedral or irregular shapes, may have faces marked with numerals or symbols instead of pips and may have their numbers carved out from the material of the dice instead of marked on it. Loaded dice are designed to favor some results over others for cheating or entertainment. History Dice have been used since before recorded history, and it is uncertain where they originated. It is theorized that dice developed from the practice ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Games Of Chance
A game of chance is in contrast with a game of skill. It is a game whose outcome is strongly influenced by some randomizing device. Common devices used include dice, spinning tops, playing cards, roulette wheels, or numbered balls drawn from a container. A game of chance may be played as gambling if players wage money or anything of monetary value. Alternatively, a game of skill is one in which the outcome is determined mainly by mental or physical skill, rather than chance. While a game of chance may have some skill element to it, chance generally plays a greater role in determining its outcome. A game of skill may also may have elements of chance, but skill plays a greater role in determining its outcome. Gambling is known in nearly all human societies, even though many have passed laws restricting it. Early people used the knucklebones of sheep as dice. Some people develop a psychological addiction to gambling, and will risk even food and shelter to continue. Some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randomization
Randomization is the process of making something random. Randomization is not haphazard; instead, a random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. For example, a random sample of individuals from a population refers to a sample where every individual has a known probability of being sampled. This would be contrasted with nonprobability sampling where arbitrary individuals are selected. In various contexts, randomization may involve: * generating a random permutation of a sequence (such as when shuffling cards); * selecting a random sample of a population (important in statistical sampling); * allocating experimental units via random assignment to a treatment or control condition; * generating random numbers (random number generation); or * transforming a data stream (such as when using a scrambler in telecommunications). Applications Randomi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brass Thumbtack
Brass is an alloy of copper (Cu) and zinc (Zn), in proportions which can be varied to achieve different mechanical, electrical, and chemical properties. It is a substitutional alloy: atoms of the two constituents may replace each other within the same crystal structure. Brass is similar to bronze, another copper alloy, that uses tin instead of zinc. Both bronze and brass may include small proportions of a range of other elements including arsenic (As), lead (Pb), phosphorus (P), aluminium (Al), manganese (Mn), and silicon (Si). Historically, the distinction between the two alloys has been less consistent and clear, and modern practice in museums and archaeology increasingly avoids both terms for historical objects in favor of the more general "copper alloy". Brass has long been a popular material for decoration due to its bright, gold-like appearance; being used for drawer pulls and doorknobs. It has also been widely used to make utensils because of its low melting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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