This article includes a list of general references, but it lacks sufficient corresponding inline citations. Please help to improve this article by introducing more precise citations.(January 2010) (Learn how and when to remove this message)
In statistics, the question of checking whether a coin is fair is one whose importance lies, firstly, in providing a simple problem on which to illustrate basic ideas of statistical inference and, secondly, in providing a simple problem that can be used to compare various competing methods of statistical inference, including decision theory. The practical problem of checking whether a coin is fair might be considered as easily solved by performing a sufficiently large number of trials, but statistics and probability theory can provide guidance on two types of question; specifically those of how many trials to undertake and of the accuracy of an estimate of the probability of turning up heads, derived from a given sample of trials.
A fair coin is an idealized randomizing device with two states (usually named "heads" and "tails") which are equally likely to occur. It is based on the coin flip used widely in sports and other situations where it is required to give two parties the same chance of winning. Either a specially designed chip or more usually a simple currency coin is used, although the latter might be slightly "unfair" due to an asymmetrical weight distribution, which might cause one state to occur more frequently than the other, giving one party an unfair advantage.[1] So it might be necessary to test experimentally whether the coin is in fact "fair" – that is, whether the probability of the coin's falling on either side when it is tossed is exactly 50%. It is of course impossible to rule out arbitrarily small deviations from fairness such as might be expected to affect only one flip in a lifetime of flipping; also it is always possible for an unfair (or "biased") coin to happen to turn up exactly 10 heads in 20 flips. Therefore, any fairness test must only establish a certain degree of confidence in a certain degree of fairness (a certain maximum bias). In more rigorous terminology, the problem is of determining the parameters of a Bernoulli process, given only a limited sample of Bernoulli trials.
^However, if the coin is caught rather than allowed to bounce or spin, it is difficult to bias a coin flip's outcome. See Gelman, Andrew; Deborah Nolan (2002). "Teacher's Corner: You Can Load a Die, But You Can't Bias a Coin". American Statistician. 56 (4): 308–311. doi:10.1198/000313002605. S2CID 123597087.
and 27 Related for: Checking whether a coin is fair information
In statistics, the question of checkingwhetheracoinisfairis one whose importance lies, firstly, in providing a simple problem on which to illustrate...
sufficient practice acoin can be made to land heads 100% of the time. Exploring the problem of checkingwhetheracoinisfairisa well-established pedagogical...
Bernoulli trials, may be called the problem of checkingwhetheracoinisfair. A Bernoulli process isa finite or infinite sequence of independent random...
Coin flipping, coin tossing, or heads or tails is the practice of throwing acoin in the air and checking which side is showing when it lands, in order...
test, involving the binomial distribution, as in checkingwhetheracoinisfair. Where extreme accuracy is not necessary, computer calculations for some...
Wickman, Forrest (9 October 2015). "Fact-Checking Steve Jobs: Was "The Customer Is Always Right" Really Coined by a Customer?". Slate. Retrieved 9 April 2024...
Suppose the task is to test whetheracoinisfair (i.e. has equal probabilities of producing a head or a tail). If the coinis flipped 100 times and the...
refinement checking, and LTL model-checking. ProB can also be used to verify properties of combined CSP and B specifications. A ProBE CSP Animator is integrated...
transaction banking account (often called a current, cheque, chequing, checking, or share draft account) where the money is held. The drawer writes various details...
organizers believed could be sold at a premium. Fair official James Ellsworth wanted the new coin to be based on a 16th-century painting he owned by Lorenzo...
authority, such as a government or bank, to uphold or maintain it. Individual coin ownership records are stored in a digital ledger, which isa computerized...
in Fair Housing Act cases. On February 8, 2013, HUD issued its Final Rule. Until 2015, the U.S. Supreme Court had not yet determined whether the Fair Housing...
economics, cash is money in the physical form of currency, such as banknotes and coins. In bookkeeping and financial accounting, cash is current assets...
have other options for payment besides a physical check, such as an electronic transfer of funds from achecking account. Depending on the issuer, the...
than directly, as with barter. Money may take a physical form as in coins and notes, or may exist as a written or electronic account. It may have intrinsic...
revising the current knowledge with A and then checkingwhether B is true in what results. Revising is easy when Ais consistent with the current beliefs...
the lake Sudarśana, which was constructed by the Mauryas for checking floods. Rudradāman is also known as the king who was ruling when the Greek writer...
good quality coin design and manufacturing can help reduce these costs. Banknotes also have an acceptance cost – the expense of checking the banknote's...
idea was to checkwhether newspapers display partisan bias, by giving more positive or negative coverage to the same economic figure, as a function of...
\\[6pt]0,&{\text{if }}\omega ={\text{tails}}.\end{cases}}} If the coinisafaircoin, Y has a probability mass function f Y {\displaystyle f_{Y}} given by:...
policy and practice, most notably on whether images that are not licensed freely may be used under a claim of fair use. Jimmy Wales has described Wikipedia...
Mental poker is the common name for a set of cryptographic problems that concerns playing afair game over distance without the need for a trusted third...
financial future in an environment of economic instability; Pursuing achecking or a savings account; Preparing for retirement or other long term expenses...
previous year— of a hypothetical Bork nomination. Conservatives were angered, but at the hearings' close Biden was praised for his fairness, humor, and courage...
Global Information